Solving Systems: Introduction to Linear Combinations

Question 1

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?

Revolt · Accepted Answer

2,921

Question 2

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?

Revolt · Accepted Answer

96

Question 3

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

Revolt · Accepted Answer

(−8, −2)

Question 4

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

Revolt · Accepted Answer

4

Question 5

The solution to the system of equation below is (−2, −1).2x − 3y = −1 11x − 9y = −13When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10.

Revolt · Accepted Answer

5x = −10 11x − 9y = −13

Question 6

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?

Revolt · Accepted Answer

15

Question 7

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

Revolt · Accepted Answer

(1, 7)

Question 8

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

Revolt · Accepted Answer

(−1, 3)

Question 9

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

Revolt · Accepted Answer

(–2, 13)

Question 10

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

Revolt · Accepted Answer

$8

Solving Systems: Introduction to Linear Combinations Answers

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