Solving Systems: Introduction to Linear Combinations

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 cost of each jersey? $5 $8 $12 $13

$8

What is the solution to this system of linear equations? 2x + y = 1 3x - y = -6 (-1, 3) (1, -1) (2, 3) (5, 0)

(-1, 3)

What is the solution to this system of linear equations? y − x = 6 y + x = −10 (−2, −8) (−8, −2) (6, −10) (−10, 6)

(-8, -2)

What is the solution to this system of linear equations? 2x + 3y = 3 7x - 3y = 24 (2, 7) (3, -21) (3, -1) (9, 0)

(3, -1)

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 both systems A and B? (3, 4) (3, 5) (4, 3) (5, 3)

(4, 3)

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= 24 3.50x + 5.00y = 97.50 Solve the system of equations. How many 10 oz. boxes were sold? 6 9 12 15

15

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 = 3,500 x - y = 2,342 Solve the system of equations. How many contemporary titles does Jarred have? 1,158 1,737 2,342 2,921

2,921

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 = 4 x + y = 18 Which two numbers did Mira pick? 10 and 8 18 and 4 20 and 16 40 and 32

20 and 16

What is the x-value in the solution to this system of linear equations? 2x − y = 11 x + 3y = −5 −3 −1 2 4

4

The solution to the system of equation below is (−2, −1). 2x − 3y = −111x − 9y = −13 When the first equation is multiplied by −3, the sum of the two equations is equivalent to 5x = −10. Which system of equations will also have a solution of (−2, −1)? 5x= −1011x − 9y= −13 2x + 9y= −1 11x − 9y= −13 −6x + 9y= −111x − 9y= −13 −6x + 3y= −15x= −10

5x= −10 11x − 9y= −13