AnswersPARTA - EOP PGCPS ALGEBRA 1 CR FALL2026 - 793023Solving Systems: Introduction to Linear Combinations

Solving Systems: Introduction to Linear Combinations Answers

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What is the solution to this system of linear equations?2x + 3y = 37x – 3y = 24

A
(2, 7)
B
(3, –21)
C
(3, –1)
D
(9, 0)
2
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Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference of the two grades is 16. The sum of one-eighth of the higher grade and one-half of the lower grade is 52. The system that represents his scores is below.x – y = 16x + y = 52What is the higher grade of Jose’s two tests?

Question illustration
A
48
B
52
C
80
D
96
3

What is the solution to this system of linear equations?2x + y = 13x – y = –6

A
(–1, 3)
B
(1, –1)
C
(2, 3)
D
(5, 0)
4

What is the solution (q, r) to this system of linear equations?12q + 3r = 15–4q – 4r = –44

A
(–18, 29)
B
(–2, 13)
C
(8, –1)
D
(15, –44)
5

Jillian is selling boxes of cookies to raise money for her basketball team. The 10 oz. box costs $3.50, while the 16 oz. box costs $5.00. At the end of one week, she collected $97.50, selling a total of 24 boxes. The system of equations that models her sales is below. x+ y= 243.50x + 5.00y = 97.50Solve the system of equations. How many 10 oz. boxes were sold?

A
6
B
9
C
12
D
15
6

Jarred sells DVDs. His inventory shows that he has a total of 3,500 DVDs. He has 2,342 more contemporary titles than classic titles. Let x represent the number of contemporary titles and y represent the number of classic titles. The system of equations models the given information for both types of DVDs.x + y = 3,500x – y = 2,342Solve the system of equations. How many contemporary titles does Jarred have?

A
1,158
B
1,737
C
2,342
D
2,921
7

Mira picked two numbers from a bowl. The difference of the two numbers was 4, and the sum of one-half of each number was 18. The system that represents Mira’s numbers is below. x – y = 4x + y = 18Which two numbers did Mira pick?

Question illustration
A
10 and 8
B
18 and 4
C
20 and 16
D
40 and 32
8

What is the x-value in the solution to this system of linear equations?2x − y = 11x + 3y = −5

A
−3
B
−1
C
2
D
4
9

A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.The system of equations that can be used to find x, the cost of each jersey, and y, the cost of each pair of shorts is shown.12x + 12y=1564x + 6y=62

A
$5
B
$8
C
$12
D
$13
10

What is the solution to this system of linear equations?x − 3y = −2x + 3y = 16

A
(7, 3)
B
(3, 7)
C
(−2, −3)
D
(−3, −2)
11

What is the solution to this system of linear equations?y − 4x = 72y + 4x = 2

A
(3, 1)
B
(1, 3)
C
(3, −1)
D
(−1, 3)
12

Mira picked two numbers from a bowl. The difference of the two numbers was 4, and the sum of one-half of each number was 18. The system that represents Mira’s numbers is below. x – y = 4x + y = 18Which two numbers did Mira pick?

Question illustration
A
10 and 8
B
18 and 4
C
20 and 16
D
40 and 32
13

What is the solution (q, r) to this system of linear equations?12q + 3r = 15–4q – 4r = –44

A
(–18, 29)
B
(–2, 13)
C
(8, –1)
D
(15, –44)
14

Kat has 19 coins, all quarters and dimes, that are worth a total of $4. The system of equations that can be used to find the number of quarters, q, and the number of dimes, d, she has is shown.q + d=190.25q + 0.1d=4

A
4
B
5
C
14
D
15
15

What is the solution to this system of linear equations?2x + y = 13x – y = –6

A
(–1, 3)
B
(1, –1)
C
(2, 3)
D
(5, 0)
16

What is the solution to this system of linear equations?y − x = 6y + x = −10

A
(−2, −8)
B
(−8, −2)
C
(6, −10)
D
(−10, 6)
17

Fiona and her friends went to a smoothie shop. They ordered three strawberry smoothies and two protein shakes for a total of $24.00. Last week they ordered one strawberry smoothie and four protein shakes for a total of $25.50. The system that represents their purchases is below.x + 4y = 25.503x + 2y = 24.00What is the price of a protein shake?

A
$3.75
B
$4.50
C
$4.95
D
$5.25
18

Jose asks his friends to guess the higher of two grades he received on his math tests. He gives them two hints. The difference of the two grades is 16. The sum of one-eighth of the higher grade and one-half of the lower grade is 52. The system that represents his scores is below.x – y = 16x + y = 52What is the higher grade of Jose’s two tests?

Question illustration
A
48
B
52
C
80
D
96
19

What is the solution (a, b) to this system of linear equations?3a+6b=452a-2b=-12

A
(-27, 6)
B
(-1, 7)
C
(1, 7)
D
(27, -6)
20

What is the x-value in the solution to this system of linear equations?2x − y = 11x + 3y = −5

A
−3
B
−1
C
2
D
4

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