Question

Breann solved the system of equations below. What mistake did she make in her work? (5 points)

2x + y = 5
x − 2y = 10

y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
5x = 20
x = 4

2(4) + y = 5
y = −3

She should have substituted 5 + 2x
She combined like terms incorrectly, it should have been 4x instead of 5x
She subtracted 10 from both sides instead of adding 10 to both sides
She made no mistake

Answer 1

let me see.... 2x + y = 5 x - 2y = 10 y = 5 - 2x (she used the 1st equation and solved for y) correct x - 2(5 - 2x) = 10 (she subbed 5 - 2x in for y in 2nd equation) correct x - 10 + 4x = 10 (she multiplied through the parenthesis) correct 5x - 10 = 10 (she combined like terms) correct 5x = 20 (she got 5x by itself) correct x = 4 (she solved for x) correct 2(4) + y = 5 (she subbed 4 in for y in the 1st equation) correct 8 + y = 5 (she skipped this step but you wouldn't need to write this) y = - 3 (she solved for y) correct check...(I am just doing this for myself) x - 2y = 10 4 - 2(-3) = 10 4 + 6 = 10 10 = 10 (correct) There is nothing wrong with Breann's answer. It is correct.