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?

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

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

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

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.

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?

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

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 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