Systems Mid-Unit Quiz Algebra 1 • Unit 5
Mid-Unit Quiz: Systems of Linear Equations
Name: ___________________________
Date: ____________ Period: ______
Maya bought 14 movie tickets for a school trip and spent a total of $132. She bought a combination of adult tickets for $12 each and student tickets for $8 each. Which system of equations below will determine the number of student tickets, \(s\), and the number of adult tickets, \(a\), she bought?
A.
\(12a + 8s = 132\)
B.
\(12a + 8s = 14\)
C.
\(8a + 12s = 132\)
D.
\(14a + 8s = 132\)
A total of 32 members are in the robotics club. The number of seventh graders in the club is 4 more than three times the number of eighth graders. Which system of equations can be used to find \(e\), the number of eighth graders, and \(s\), the number of seventh graders?
A.
\(e + s = 32\)
B.
\(e + s = 32\)
C.
\(e + s = 32\)
D.
\(e + s = 32\)
Given the system of equations below:
\[y = -\frac{3}{4}x + 2\] \[5x + 4y = -4\]
What is the \(x\)-value of the solution? Show your work in the space below.
\(x =\)
Which graph represents the system of equations?
\[2x - y = 2\] \[-x = 3y - 15\]
A. -8-448 84-4-8
B. -8-448 84-4-8
C. -8-448 84-4-8
D. -8-448 84-4-8
Elena and Marcus are buying supplies for an art fundraiser. Elena bought 4 sketchbooks and 6 packs of markers for a total of $62. Marcus bought 7 sketchbooks and 3 packs of markers for a total of $56.
What is the cost of one sketchbook and one pack of markers? Show your work below.
One sketchbook costs $
One pack of markers costs $
The tables of ordered pairs represent some points on the graphs of lines \(f(x)\) and \(g(x)\). What is the solution to the system of equations represented in these tables?
x
f(x)
-1
-5
0
-2
1
1
2
4
3
7
x
g(x)
-2
8
0
6
2
4
4
2
6
0
A. \((0, -2)\)
B. \((0, 6)\)
C. \((2, 4)\)
D. \((-2, 6)\)
Graph the linear function on the coordinate grid below.
\[y = -\frac{2}{3}x + 4\]
-8-6-4-2 2468 8642 -2-4-6-8
Graph the linear function on the coordinate grid below.
\[y = \frac{3}{2}x - 3\]
-8-6-4-2 2468 8642 -2-4-6-8
Given the system of equations below:
\[3x - 2y = 16\] \[x + 2y = 8\]
What is the \(y\)-value of the solution? Show your work in the space below.
\(y =\)
Systems Quiz Answer Key Algebra 1 • Unit 5 • Teacher Resource
Mid-Unit Quiz: Answer Key & Solutions
Items 1–6
1. Answer: A TEKS A1.2I
Solution: Total tickets gives \(a + s = 14\). Total cost at $12 per adult ticket and $8 per student ticket gives \(12a + 8s = 132\).
2. Answer: B TEKS A1.2I
Solution: Total members gives \(e + s = 32\). "Seventh graders (\(s\)) is 4 more than three times eighth graders (\(e\))" translates to \(s = 3e + 4\).
3. Answer: \(x = -6\) TEKS A1.5C
Solution: Substitute \(y = -\frac{3}{4}x + 2\) into \(5x + 4y = -4\):
4. Answer: C TEKS A1.3F
Solution: Rewrite both equations in slope-intercept form:
5. Answer: Sketchbook = $5 (or 5.00); Markers = $7 (or 7.00) TEKS A1.5C
Solution: Set up \(4s + 6m = 62\) and \(7s + 3m = 56\).
6. Answer: C — \((2, 4)\) TEKS A1.5C
Solution: Both tables contain the shared ordered pair \((2, 4)\), meaning \(f(2) = 4\) and \(g(2) = 4\).
Algebra 1 • Unit 5 • Teacher Resource
Mid-Unit Quiz: Answer Key & Solutions
Items 7–9
7. Graph of \(y = -\frac{2}{3}x + 4\) TEKS A1.3C
Key Features:
\(y\)-intercept: \((0, 4)\)
Slope: \(m = -\frac{2}{3}\) (down 2, right 3)
Additional points: \((-3, 6)\), \((3, 2)\), \((6, 0)\)
8. Graph of \(y = \frac{3}{2}x - 3\) TEKS A1.3C
Key Features:
\(y\)-intercept: \((0, -3)\)
Slope: \(m = \frac{3}{2}\) (up 3, right 2)
Additional points: \((-2, -6)\), \((2, 0)\), \((4, 3)\), \((6, 6)\)
9. Answer: \(y = 1\) TEKS A1.5C
Solution: Add the two equations to eliminate \(y\):
Systems Jeopardy Word Problems Algebra 1 • Unit 5 • Review Game Bank
Jeopardy Word Problems: Systems of Equations
15 Prompts
Category 1: Build the System
TEKS A1.2I
$100
A bakery sold 25 muffins and bagels combined for a total of $61. Muffins cost $3 each and bagels cost $2 each. Write a system of equations to find \(m\), the number of muffins, and \(b\), the number of bagels.
$200
At a school concert, there are 48 people in the audience. The number of adults, \(a\), is 6 more than twice the number of children, \(c\). Write a system of equations to represent this situation.
$300
Jordan has 18 coins in his pocket consisting of nickels, \(n\), and quarters, \(q\). The total value of the coins is $3.10. Write a system of equations to determine the number of each coin.
$400
A rectangular garden has a perimeter of 54 feet. The length, \(l\), is 3 feet less than twice the width, \(w\). Write a system of equations to find the dimensions of the garden.
$500
Two streaming services offer different plans. Plan A charges a $15 setup fee plus $8 per month. Plan B charges no setup fee and $11 per month. Write a system of equations for the total cost, \(y\), after \(x\) months for both plans.
Category 2: Price & Ticket Mix-Ups
TEKS A1.5C
$100
Noah bought 3 tacos and 2 burritos for $19. Ava bought 3 tacos and 4 burritos for $29. What is the cost of one burrito?
$200
A zoo sold 120 tickets on Friday for a total of $1,080. Adult tickets cost $12 and child tickets cost $7. How many adult tickets were sold?
Category 2: Price & Ticket Mix-Ups (continued)
TEKS A1.5C
$300
At a farmer's market, 2 pounds of apples and 5 pounds of peaches cost $23. Three pounds of apples and 2 pounds of peaches cost $18. What is the cost of 1 pound of apples?
$400
Liam spent $44 on 4 notebooks and 8 pens. Chloe spent $31 on 3 notebooks and 5 pens. What is the combined cost of 1 notebook and 1 pen?
$500
A theater sold 85 tickets for a matinee show, collecting $735. Floor seats cost $11 and balcony seats cost $7. How many more balcony seats than floor seats were sold?
Category 3: Compare & Conquer
TEKS A1.5C
$100
The sum of two numbers is 42, and their difference is 10. What are the two numbers?
$200
A gym offers two membership options. Option A costs $40 to join plus $25 per month. Option B costs $10 to join plus $30 per month. After how many months will both options cost the same?
$300
The perimeter of a rectangular soccer field is 320 yards. The length is 40 yards longer than the width. Find the length and width of the field.
$400
Two cars leave the same city heading east. Car A travels at 55 mph and leaves 1 hour before Car B, which travels at 65 mph. How many hours after Car B leaves will it catch up to Car A?
$500
A science lab needs 20 liters of a 30% acid solution. The lab has a 20% acid solution and a 45% acid solution. How many liters of each solution should be mixed?
Algebra 1 • Unit 5 • Host Reference
Jeopardy Answer Key
All 15 Answers
Category 1: Build the System
$100: \(m + b = 25\) and \(3m + 2b = 61\)$200: \(a + c = 48\) and \(a = 2c + 6\)$300: \(n + q = 18\) and \(0.05n + 0.25q = 3.10\)$400: \(2l + 2w = 54\) and \(l = 2w - 3\)$500: \(y = 8x + 15\) and \(y = 11x\)
Category 2: Price & Ticket Mix-Ups
$100: $5 per burrito. \((3t + 4b) - (3t + 2b) = 29 - 19 \Rightarrow 2b = 10 \Rightarrow b = 5\).$200: 48 adult tickets . \(a + c = 120\) and \(12a + 7c = 1080 \Rightarrow 5a = 240 \Rightarrow a = 48\).$300: $4 per pound of apples. \(2a + 5p = 23\) and \(3a + 2p = 18 \Rightarrow 11a = 44 \Rightarrow a = 4\).$400: $9 combined ($7 notebook + $2 pen). \(n + 2p = 11\) and \(3n + 5p = 31 \Rightarrow p = 2, n = 7\).$500: 15 more balcony seats (50 balcony, 35 floor). \(f + b = 85\) and \(11f + 7b = 735 \Rightarrow 4b = 200 \Rightarrow b = 50, f = 35\).
Category 3: Compare & Conquer
$100: 26 and 16 . \(x + y = 42\) and \(x - y = 10 \Rightarrow 2x = 52 \Rightarrow x = 26, y = 16\).$200: 6 months (total cost $190). \(40 + 25m = 10 + 30m \Rightarrow 30 = 5m \Rightarrow m = 6\).$300: Length = 100 yd, Width = 60 yd . \(l + w = 160\) and \(l = w + 40 \Rightarrow 2w + 40 = 160 \Rightarrow w = 60, l = 100\).$400: 5.5 hours (5 hours 30 minutes). \(55(t + 1) = 65t \Rightarrow 10t = 55 \Rightarrow t = 5.5\).$500: 12 L of 20% solution and 8 L of 45% solution . \(x + y = 20\) and \(0.20x + 0.45y = 6 \Rightarrow 5y = 40 \Rightarrow y = 8, x = 12\). 
