Question

Carlos solved the system of equations below. What mistake did he make in his work?

2x + y = 5
x − 2y = 10

y = 5 − 2x
x − 2(5 − 2x) = 10
x + 10 + 4x = 10
5x + 10 = 10
5x = 0
x = 0

2(0) + y = 5
y = 5

He should have substituted 5 + 2x

He did not distribute correctly

He combined like terms incorrectly, it should have been 4x instead of 5x

He made no mistake

Answer 1

The mistake starts at the part when -2(5-2x)
The consequent equation should be -10+4x and not +10+4x

Answer 2

so he should have substituted 5 +2x?

Answer 3

^^

Answer 4

No. y = 5 − 2x is correct.

Answer 5

so He did not distribute correctly is it right

Answer 6

He distributed correctly.
Take a look at this.

2x + y = 5
2x + y -2x = 5 -2x
y = 5 - 2x

Answer 7

cause its not the 3rd choice because i chose that last time and it was wrong

Answer 8

so he made no mistake then

Answer 9

He did make a mistake but it's not in all four of the choices.

Answer 10

I've already written the mistake in my first reply here.

Answer 11

i know but thats not in the choices of the answer options

Answer 12

Since there's a mistake (4th choice out), and the 1st and 3rd choices aren't correct too, so the 2nd choice should be the best answer.

Answer 13

okay so he didnt distribute correctly

Answer 14

I do not know what "distribute" here means anyway. Seems to me it isn't like converting the wrong sign.

Answer 15

soo.. it would be the second one?

Answer 16

Yeah

Answer 17

Yes. The only logical answer after deducting all the confirmed-to-be wrong ones.