Question

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

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

I just took the test and the answer is She made no mistake

Explanation:

Answer 2

If 2x+y=5, then y=5-2x, so she substituted correctly.
x+4x=5x, so she combined like terms correctly.
She didn't subtract 10 from both sides, she added 10 to both sides.

Check the solution:

`2x+y=5 \hbox{ and } x-2y=10 \\ 2 * 4-3=5 \hbox{ and } 4-2 * (-3)=10 \\ 8-3=5 \hbox{ and } 4+6=10 \\ 5=5 \hbox{ and } 10=10 \\ \checkmark`

The answer is: She made no mistake.