Algebra 1 Workbook — Chapter 8: Systems of Two Linear Equations

SOL A.EI.2 (a, b, c, h) · Companion to Textbook Chapter 8

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/. Every numbered item is the same problem as in the textbook, so one answer key serves both. Item numbers run continuously from 1 to 132.

PAGE 1 — Chapter opener

Chapter 8 · Systems of Two Linear Equations

Standard A.EI.2 (a, b, c, h)

In this chapter you will:

Create a system of two linear equations from a situation, defining variables with units
Test whether an ordered pair is a solution — it must satisfy both equations
Solve a system by graphing, by substitution, and by elimination
Decide whether a system has one solution, no solution, or infinitely many
Verify a solution algebraically, graphically, and with technology
Explain your method and interpret the solution in context, with units

Words to know: system of two linear equations · solution of a system · ordered pair · verify · point of intersection · substitution · back-substitute · elimination · addition property of equality · equivalent equation · one solution · no solution · infinitely many solutions · parallel lines · identical lines · break-even point · viewing window · interpret

Convention: a solution of a system is an ordered pair, never a single number. " $x = 3$ " is half an answer. Check every candidate in both original equations.

PAGE 2 — What a system is

8.1 A System and Its Solution

FIGURE: fig1-a-system-and-its-solution.png (full width)

Fill in the blanks.

A solution of a system is an ordered pair that makes ____________ equations true.

On a graph, the solution is the point where the two lines ____________________.

Solution of $x - y = -1$ and $2x + y = 7$ : ____________

What names it on the graph? _______________________________________
Verify it.

Equation	Substitute	True?
$x - y = -1$
$2x + y = 7$

Is $(0,1)$ a solution? ______ Show both substitutions:

PAGE 3 — One equation is not enough

Checking Against Both Lines

FIGURE: fig7-checking-a-candidate-point.png (full width)

Which of $(2,3)$ and $(4,1)$ solves $x + y = 5$ and $2x - y = 1$ ?

Point	$x + y = 5$	$2x - y = 1$	Solution?
$(2,3)$
$(4,1)$

Explain. Why must an ordered pair satisfy both equations?

PAGE 4 — Building a system from a story

Creating a System

Three steps. ① Define each variable in a ____________ sentence, with ____________. ② Find the two independent ____________. ③ Write one ____________ per fact.

Adult tickets $12, child tickets $8; $40$ tickets sold for $408.

Let $a$ = _______________________________________

Let $c$ = _______________________________________

Tickets: _______________________ Dollars: _______________________
Apply it. $12$ coins, nickels and dimes, worth $95$ cents.

Let $n$ = ____________________ Let $d$ = ____________________

Coins: ____________________ Cents: ____________________
Apply it. Rectangle, perimeter $34$ cm, length $5$ cm more than width.

Let $L$ = ____________________ Let $W$ = ____________________

Perimeter: ____________________ Relationship: ____________________
Apply it. A class of $27$ has $3$ more than twice as many boys as girls.

System: ____________________ and ____________________

PAGE 5 — Practice · testing pairs

Practice · Is It a Solution?

System: $3x + y = 11$ and $x - 2y = 6$ .

Pair	First equation	Second equation	Solution?
a) $(4,-1)$
b) $(2,5)$
c) $(0,11)$
d) $(-2,-4)$

Verify $(-3,2)$ in $2x + 5y = 4$ and $x - y = -5$ : _______________________________________
Apply it. Ride Rite: $3 plus $2 per mile. Cab Co: $7 plus $1 per mile.

Let $x$ = ____________________ Let $y$ = ____________________

System: ____________________ and ____________________
Explain. Why can a system of two linear equations never have exactly two solutions?
Find the error. A student says $(1,4)$ solves $x + y = 5$ and $2x - y = 4$ "because $1 + 4 = 5$ ."

What went wrong? _______________________ Correct solution: ____________
Technology. Steps to check $(4,-1)$ in $3x + y = 11$ , $x - 2y = 6$ on a calculator:
Apply it. $3$ notebooks and $2$ pens cost $13; $5$ notebooks and $4$ pens cost $23.

Let $n$ = ____________________ Let $p$ = ____________________

System: ____________________ and ____________________

PAGE 6 — Exit ticket 8.1

Exit Ticket · Lesson 8.1

Name: ________________________ Date: ____________

Is $(5,-2)$ a solution of $x + y = 3$ , $2x + 3y = 4$ ? ______ Show both: ____________
Is $(1,6)$ a solution of $y = 4x + 2$ , $3x + y = 10$ ? ______ Show both: ____________
$9$ fish, twice as many tetras as guppies. System: ____________ and ____________
Explain. What is a solution of a system, and why is it an ordered pair?

PAGE 7 — Solving by graphing

8.2 Solving a System by Graphing

FIGURE: fig6-graphing-a-system.png (full width)

Four steps. ① Solve each equation for ______. ② Graph ______ lines. ③ Read the ____________ point. ④ ____________ in both original equations.

$2x + y = 8 \rightarrow$ ____________________ $x - y = 1 \rightarrow$ ____________________

Solution: ____________
Verify in the originals: _______________________________________
From the one-solution figure: solution of $y = 2x - 3$ , $y = -x + 3$ : ____________

Verify: _______________________________________

PAGE 8 — Graphing practice

Practice · Read the Crossing

FIGURE: fig11-blank-grids-systems.png (full page, use Grids A–D)

$y = x + 2$ and $y = -2x + 5$ Solution: ____________ Verified? ______
$y = \tfrac12 x - 1$ and $y = -x + 5$ Solution: ____________ Verified? ______
Solve each by graphing.

System	Solution	Check in both?
a) $y = x - 4$ , $y = -2x + 5$
b) $y = -3x + 2$ , $y = x - 6$
c) $x + y = 1$ , $y = 2x + 4$
d) $y = \tfrac12 x + 1$ , $y = -\tfrac12 x + 3$

Rewrite, then graph.

System	Slope-intercept forms	Solution
a) $3x + y = 5$ , $x - y = 3$
b) $x + 2y = 8$ , $y = x - 2$
c) $2x - y = 4$ , $x + y = 5$

$y = 2x + 1$ and $y = 2x - 3$ Number of solutions: ____________ Why? ____________
$y = -x + 3$ and $2x + 2y = 6$ Number of solutions: ____________ Why? ____________

PAGE 9 — The window that lies

When the Picture Is Incomplete

FIGURE: fig9-window-that-lies.png (full width — do not place text beside it)

Explain. What does the left panel appear to show? Why is that reading wrong?

What did the slopes tell you first? _______________________________________
Technology. Graph $y = 1.5x + 2$ and $y = 1.6x - 2$ .

Window used: ____________________ Intersection: ____________

Algebraic confirmation: _______________________________________
Explain. When does graphing give an exact answer, and what should you do when it does not?
Find the error. A student graphs $y = 3x - 1$ and $y = 3x + 4$ and reports "about $(6,17)$ ."

What went wrong? _______________________ Correct answer: ____________

PAGE 10 — Systems in a context graph

Reading a Break-Even Point

FIGURE: fig8-context-two-ride-plans.png (half width)

Apply it. Solution: ____________

In a sentence, with units: _______________________________________

Cheaper for $2$ miles: ____________ Cheaper for $10$ miles: ____________
Apply it. Dana: $60 saved, $5 a week. Eli: $100 saved, $3 a week.

System: ____________________ and ____________________

Window needed: ____________________ Solution: ____________
Apply it. Cost $y = 4x + 120$ ; revenue $y = 10x$ .

Solution: ____________ What it means: _______________________________________
Graph $x = -2$ and $y = 4$ . Solution: ____________

Why can $x = -2$ not be written as $y = mx + b$ ? _______________________________________

PAGE 11 — Exit ticket 8.2

Exit Ticket · Lesson 8.2

Name: ________________________ Date: ____________

$y = x - 1$ , $y = -x + 5$ Solution: ____________ Verified? ______
$x + y = 4$ , $y = 2x + 1$ Solution: ____________ Verified? ______
Two lines both fall $4$ units per $1$ unit right and cross the $y$ -axis at different points.

Number of solutions: ____________ Why? _______________________________________
Technology. No crossing on the standard window, but the slopes differ. Conclusion and next step:

PAGE 12 — Substitution

8.3 Solving by Substitution

Five steps. ① ____________ one variable in one equation. ② Substitute into the ____________ equation. ③ Solve the ____________-variable equation. ④ ____________-substitute. ⑤ Write the ____________ pair and verify.

$y = 3x - 2$ , $2x + y = 8$

Substituted equation: _______________________ $x =$ ______ $y =$ ______ Pair: ____________
$x = y + 3$ , $2x + 5y = 13$ Pair: ____________
$y = -2x + 9$ , $y = 4x - 3$ Set equal: _______________________ Pair: ____________
$x + y = 7$ , $3x - 2y = 6$ Isolated: ____________________ Pair: ____________
Verify item 45.

Equation	Substitute	True?
$x + y = 7$
$3x - 2y = 6$

Explain. Why is substitution easiest when a variable has coefficient $1$ or $-1$ ?

PAGE 13 — Substitution practice

Practice · Substitute and Solve

A variable is already isolated.

System	Substituted equation	Solution
a) $y = 2x + 1$ , $3x + y = 11$
b) $x = 3y - 1$ , $2x + y = 12$
c) $y = -x + 6$ , $4x - y = 9$
d) $y = 5x$ , $x + y = 18$

Isolate first. Say which variable you chose and why.

System	Variable isolated	Solution
a) $x + 2y = 11$ , $3x - y = 5$
b) $2x + y = -1$ , $5x - 3y = 25$
c) $x - 4y = -2$ , $3x + 2y = 8$

$y = 3x + 1$ , $6x - 2y = 5$ Statement you end with: ____________

Solutions: ____________________ Picture: ____________________
$y = -4x + 5$ , $8x + 2y = 10$ Statement you end with: ____________

Solutions: ____________________ Picture: ____________________

PAGE 14 — Substitution in context

Apply It · Substitution

Apply it. Two numbers: sum $46$ , difference $12$ .

System: ____________________ and ____________________ Numbers: ______ and ______
Apply it. Solve your item 11 rectangle. Width: ______ cm Length: ______ cm
Apply it. Solve your item 12 class. Boys: ______ Girls: ______
Apply it. Plan A: $25 plus $0.10 per minute. Plan B: $15 plus $0.15 per minute.

System: ____________________ and ____________________ Solution: ____________

In a sentence, with units: _______________________________________
Explain. Name a system where substitution is clearly better, and one where it is painful.
Find the error. A student substitutes $y = 2x - 1$ back into that same equation and gets $2x - 1 = 2x - 1$ .

What went wrong? _______________________________________________

Correct work with $4x - 2y = 2$ : _______________________ Solutions: ____________
$y = x + 4$ , $3x + 2y = 23$ Solution: ____________ Graphical confirmation: ____________

PAGE 15 — Exit ticket 8.3

Exit Ticket · Lesson 8.3

Name: ________________________ Date: ____________

$y = 4x - 7$ , $2x + y = 11$ Solution: ____________
$x = 2y + 1$ , $3x - y = 8$ Solution: ____________
$x + y = 9$ , $2x - y = 3$ Isolated: ____________ Solution: ____________
Apply it. Solve your item 19 fish tank. Guppies: ______ Tetras: ______

PAGE 16 — Elimination

8.4 Solving by Elimination

Five steps. ① Line up ____________ terms. ② Make one pair of coefficients ____________. ③ ____________ the equations. ④ Solve for the surviving variable. ⑤ Back-substitute, write the pair, and ____________.

$x + y = 10$ , $x - y = 4$ Sum: ____________ Solution: ____________
$3x + 2y = 16$ , $x - 2y = 0$ Sum: ____________ Solution: ____________
$2x + 3y = 12$ , $x - y = 1$ Multiplied ______ by ______ Solution: ____________
$3x + 4y = 10$ , $2x + 3y = 7$ Multipliers: ______ and ______ Solution: ____________
Verify item 66.

Equation	Substitute	True?
$3x + 4y = 10$
$2x + 3y = 7$

Explain. Why does adding the two equations give a true equation? Name the property.

PAGE 17 — Elimination practice

Practice · Eliminate a Variable

Add or subtract as they stand.

System	Variable eliminated	Solution
a) $x + y = 12$ , $x - y = 2$
b) $2x + y = 9$ , $3x - y = 11$
c) $5x + 2y = 11$ , $3x - 2y = 13$
d) $7x + 4y = 2$ , $3x - 4y = 18$

Multiply one equation first.

System	Multiplier	Solution
a) $x + 3y = 7$ , $2x - y = 7$
b) $4x + y = 10$ , $3x - 2y = 13$
c) $5x - 2y = 4$ , $3x + y = 9$

Multiply both equations.

System	Multipliers	Solution
a) $2x + 3y = 13$ , $3x + 2y = 12$
b) $4x + 5y = 7$ , $3x - 2y = -12$

$2x + y = 5$ , $4x + 2y = 3$ Ends with: ____________ Solutions: ____________ Graph: ____________
$3x - y = 6$ , $6x - 2y = 12$ Ends with: ____________ Solutions: ____________ Graph: ____________

PAGE 18 — Elimination in context

Apply It · Elimination

FIGURE: fig10-context-tickets-system.png (half width)

Apply it. Solve your item 16 notebooks and pens. Notebook: $______ Pen: $______
Apply it. Solve your item 5 theater. Adult: ______ Child: ______
Apply it. Solve your item 9 coins. Nickels: ______ Dimes: ______
Apply it. $12$ tickets, $50 taken in, adult $5 and student $3.

System: ____________________ and ____________________ Solution: ____________

Does it match the marked point on the figure? ______
Explain. Why does multiplying one equation by a nonzero number leave the solution set unchanged? What goes wrong at $0$ ?
Find the error. Subtracting $3x + 2y = 5$ from $5x + 2y = 11$ , a student writes $2x = 16$ .

What went wrong? _______________________ Solution: ____________

PAGE 19 — Exit ticket 8.4

Exit Ticket · Lesson 8.4

Name: ________________________ Date: ____________

$x + y = 8$ , $x - y = 2$ Solution: ____________
$2x + 3y = 7$ , $4x - 3y = 5$ Solution: ____________
$3x + 2y = 4$ , $x - y = 3$ Multiplier: ______ Solution: ____________
Apply it. Five hot dogs and two drinks cost $17; three hot dogs and four drinks cost $20.

System: ____________________ and ____________________

Hot dog: $______ Drink: $______

PAGE 20 — The three cases

8.5 One, None, or Infinitely Many

FIGURE: fig5-three-cases-side-by-side.png (full width — do not place text beside it)

Complete the table.

Case	Slopes	$y$ -intercepts	Algebra ends with	Solutions
Intersecting
Parallel
Identical

Name the three cases shown, left to right: ____________, ____________, ____________

PAGE 21 — Each case up close

One, None, Infinitely Many

FIGURE: fig2-system-one-solution-intersecting.png (one-third width)

Classify, and justify with the slopes: _______________________________________

FIGURE: fig3-system-no-solution-parallel.png (one-third width)

Classify, and justify with slopes and intercepts: _______________________________________

FIGURE: fig4-infinitely-many-same-line.png (one-third width)

Classify, and show that one equation is a multiple of the other:
$y = 3x + 1$ , $y = 3x - 4$ Classification: ____________________ How you decided: ____________
$2x - 4y = 6$ , $x - 2y = 3$ Classification: ____________________ How you decided: ____________

PAGE 22 — Classification practice

Practice · Count the Solutions

Compare slopes and intercepts.

System	Slopes	Intercepts	Solutions
a) $y = -2x + 7$ , $y = 5x - 1$
b) $y = \tfrac14 x - 3$ , $y = \tfrac14 x + 2$
c) $y = -x + 8$ , $3x + 3y = 24$
d) $4x + y = 9$ , $y = -4x + 1$
e) $x + y = 6$ , $x - y = 6$

Rewrite in slope-intercept form, then classify.

System	Rewritten	Solutions
a) $2x + 3y = 6$ , $4x + 6y = 12$
b) $2x + 3y = 6$ , $4x + 6y = 18$
c) $2x + 3y = 6$ , $4x - 6y = 12$

$y = kx + 3$ , $y = 5x - 2$ has no solution when $k =$ ______

Why can no $k$ give infinitely many? _______________________________________
$y = 2x + c$ , $4x - 2y = -6$ has infinitely many when $c =$ ______

Every other $c$ gives ____________________ because _______________________

PAGE 23 — Classification in context and errors

Apply It · What the Count Means

Apply it. Shop A: $45 plus $3 per shirt. Shop B: $60 plus $3 per shirt.

System: ____________________ and ____________________ Classification: ____________

What it means for a customer: _______________________________________
Explain. Why can a system of two linear equations never have exactly three solutions?
Find the error. A student reaches $0 = 0$ and writes "no solution."

What went wrong? _______________________ Correct conclusion: ____________________
Explain. Connect "the variables vanished and left a false statement" to "the lines are parallel."

PAGE 24 — Exit ticket 8.5

Exit Ticket · Lesson 8.5

Name: ________________________ Date: ____________

$y = -3x + 2$ , $y = -3x + 2$ Solutions: ____________ Graph: ____________________
$x - y = 4$ , $2x - 2y = 9$ Solutions: ____________ Graph: ____________________
$5x + y = 3$ , $x - y = 3$ Solutions: ____________ If one, find it: ____________
Explain. The difference between ending with $0 = 0$ and ending with $0 = 7$ :

PAGE 25 — The five-step model

8.6 Modeling with Systems

FIGURE: fig10-context-tickets-system.png (half width)

Five steps. ① Define both variables in full ____________, with ____________. ② One equation per independent ____________. ③ ____________, and say why you chose that method. ④ Verify ____________ ways. ⑤ ____________ the pair as a sentence.

Apply it. Adult tickets $5, student tickets $3; $12$ tickets, $50.

Let $x$ = _______________________ Let $y$ = _______________________

System: ____________________ and ____________________ Solution: ____________

Sentence: _______________________________________
Apply it. Use the ride-plan figure. Variables, system, solution, and what each side of the crossing means:

PAGE 26 — Verifying three ways

Three Kinds of Evidence

$30$ marbles, $6$ more blue than red. System: ____________ and ____________ Solution: ____________
Verify item 104 three ways.

Check	What you do	What you find
Algebraically
Graphically
With technology

Explain your method. Name the method, the reason, the key step, and the check.
$5$ vehicles — vans hold $6$ , buses hold $20$ — carry $78$ people.

System: ____________________ and ____________________ Solution: ____________

Why it cannot describe the trip: _______________________________________

PAGE 27 — Modeling practice

Apply It · Build, Solve, Interpret

Apply it. Gym A: $50 to join, $20 a month. Gym B: $20 to join, $25 a month.

System: ____________ and ____________ Solution: ____________ Sentence: ____________
Apply it. Garden perimeter $96$ ft, length three times the width.

System: ____________ and ____________ Length: ______ ft Width: ______ ft
Apply it. $20$ bills, twos and fives, worth $70.

System: ____________ and ____________ Twos: ______ Fives: ______
Apply it. A $20$ -cm candle burns $2$ cm per hour; a $14$ -cm candle burns $0.5$ cm per hour.

System: ____________ and ____________ Solution: ____________

Sentence: _______________________________________
Technology. Check item 111. Window: ____________ Reported point: ____________ Agrees? ______

PAGE 28 — Reasoning and errors

Explain and Correct

Explain. Why does substituting into only one equation prove nothing?
Find the error. A student finds $x = 9$ and writes "the solution is $9$ ."

What is missing? _______________________________________________

A complete answer looks like: _______________________________________
Apply it. Shop A: $45 plus $3 per shirt. Shop B: $60 plus $3 per shirt.

Solution: ____________________ What it means for a customer: ____________________
Apply it. " $2$ lb trail mix and $1$ lb nuts for $14" and " $4$ lb trail mix and $2$ lb nuts for $28."

System: ____________ and ____________ Classification: ____________________

Why the second ad adds nothing: _______________________________________

PAGE 29 — Exit ticket 8.6

Exit Ticket · Lesson 8.6

Name: ________________________ Date: ____________

Apply it. $15$ questions worth $2$ or $5$ points each, $51$ points total.

Let $x$ = _______________________ Let $y$ = _______________________

System: ____________ and ____________ Solution: ____________
Verify algebraically in both, and describe the graphical check:
Interpret in one sentence with units: _______________________________________
Technology. How you would confirm it, and what a different reported point would mean:

PAGE 30 — Chapter 8 review · creating and solving

Chapter 8 Review

Part A · Creating a system from a context

Apply it. Pencils $0.50, erasers $0.75; $40$ items sold for $25.

Let $p$ = ____________________ Let $e$ = ____________________

System: ____________ and ____________ Solution: ____________
Apply it. Sum $32$ ; the larger is $7$ less than twice the smaller.

System: ____________ and ____________ Numbers: ______ and ______

Part B · Solving algebraically and graphically

$y = -x + 1$ , $y = 2x - 5$ by graphing Solution: ____________ Verified? ______
$y = 3x - 4$ , $x + 2y = 13$ by substitution Solution: ____________
$3x + 2y = 11$ , $2x - 2y = 14$ by elimination Solution: ____________
$4x - 3y = -1$ , $2x + y = 7$ by any method Method: ____________ Why: ____________ Solution: ____________

PAGE 31 — Chapter 8 review · counting, verifying, interpreting

Chapter 8 Review (continued)

Part C · Counting the solutions

FIGURE: fig5-three-cases-side-by-side.png (full width)

$y = \tfrac12 x + 4$ , $x - 2y = 10$ Solutions: ____________ Graph: ____________________
$6x + 2y = 8$ , $y = -3x + 4$ Solutions: ____________ Graph: ____________________
$x + y = 5$ , $x - y = 1$ Solutions: ____________ If one, find it: ____________

Part D · Verifying, explaining, interpreting

Verify your item 126 answer three ways.

Check	What you do	What you find
Algebraically
Graphically
With technology

Apply it. Tank A: $500$ L draining $20$ L per minute. Tank B: $200$ L filling $10$ L per minute.

System: ____________ and ____________ Solution: ____________

Sentence: _______________________________________
Explain. Method, reason, key step, three-way verification, and whether the answer is reasonable:

PAGE 32 — Blank grids

Graph Paper

FIGURE: fig11-blank-grids-systems.png (full page)

Use these grids for any system a teacher assigns alongside this chapter: graphing two lines to find where they cross, checking an algebraic answer against a picture, or drawing the parallel pair that shows why a system has no solution.

Three reminders for every sketch:

Solve each equation for $y$ before graphing, then plot from the $y$ -intercept using the slope.
Mark the crossing point and label it as an ordered pair, not as a single number.
A reading off a grid is a claim. Finish by substituting the pair into both original equations.

Canva production notes

Page size: 8.5 × 11 in, 0.75 in margins
Type: headings 24–28 pt, body 12–14 pt, answer blanks 14 pt with 1.5 line spacing
Item order: a few items are placed by figure rather than by number, so that every item on a page can be answered from the figure on that page. Page 3 runs 4 then 6; page 4 runs 5, 9, 11, 12; page 5 runs 7, 8, 10, 13–16; page 9 places 26 before 33–35; page 21 runs 85–89 beside the three case figures. The numbers still match the textbook exactly, and the answer key is in numerical order.
Figure widths: fig1-a-system-and-its-solution.png, fig6-graphing-a-system.png, and fig7-checking-a-candidate-point.png are full width on first appearance. fig5-three-cases-side-by-side.png and fig9-window-that-lies.png are wide multi-panel images — set them full width and do not place text beside them, or the panels shrink below readable. On page 21 the three single-case figures sit in a row at one-third width each; if that crowds the labels, stack them and let the page run to two columns instead. fig10-context-tickets-system.png repeats on pages 18 and 25, and fig5 repeats on page 31; repeat the image rather than asking students to flip back. fig11-blank-grids-systems.png takes a full page on its own and is also referenced from page 8.
The graphing pages need real grids. Items 24, 25, 27, 28, 29, 30, and 37 are all solve by graphing, and there is no room to draw two lines in a text blank. Place the four grids of fig11-blank-grids-systems.png on page 8 and label which grid goes with which item, or add a second copy of that page.
Blank work space: items 6, 13, 20, 26, 34, 40, 41, 47, 56, 57, 68, 78, 92, 93, 95, 96, 97, 101, 106, 113, 114, 116, 120, and 132 are written explanations — give each at least four ruled lines, not a single blank. Item 132 asks for five separate things and needs eight lines.
Ordered pairs versus single numbers: every blank labeled "Solution" must be wide enough for an ordered pair with parentheses and a comma, and should be pre-printed with the parentheses — (______ , ______) — because reporting a single number is this chapter's most common error and the blank itself can prevent it.
Verification tables appear on pages 2, 3, 12, 16, 26, and 31. Keep all three rows of the three-way tables on one page; splitting "with technology" onto the next page is what makes students skip it.
Fractions: items 25, 27d, 86, 90b, 91, 93, and 127 have fractional slopes. Set them as stacked fractions, not slashes, so that $\tfrac12$ never reads ambiguously across a line break.
Negative signs: use the typographic minus (−), matching the figures, not a hyphen.
Currency: dollar amounts appear on pages 4, 5, 10, 14, 18, 19, 23, 27, 28, and 30. Set them as plain text ($12, $8, $408, $3, $2, $7, $13, $23, $25, $15, $17, $20, $45, $60, $50, $70, $14, $28, $0.50, $0.75), not inside a math box.