Solving Systems: Introduction to Linear Combinations Answers

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?

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

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

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

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

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?

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