Solving Systems: Introduction to Linear Combinations Answers

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?

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?

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

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

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

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

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

Two systems of equations are shown. The first equation in system B is the original equation in system A. The second equation in system B is the sum of that equation and a multiple of the second equation in system A.

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

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