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

Could someone help me figure this out please?

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

Could someone help me figure this out please?

anonymous · Answer

User: Marshall Davis 
In Course: Algebra I V20 ( 4077)
Instructor: Donna Schroeder
Exam: 05.04 Module Five Quiz
Warning: There is a checkbox at the bottom of the exam form that you MUST check prior to submitting this exam. Failure to do so may cause your work to be lost.

Question 1 (Multiple Choice Worth 5 points)

(05.01 LC)

Systems of equations with different slopes and different y-intercepts have more than one solution.

 Always
 Sometimes
 Never
Question 2 (Multiple Choice Worth 5 points)

(05.02 MC)

What is the value of the x variable in the solution to the following system of equations?

2x − 3y = 3
5x − 4y = 4

 −1
 0
 x can be any number as there are infinitely many solutions to this system
 There is no x value as there is no solution to this system
Question 3 (Multiple Choice Worth 5 points)

(05.02 MC)

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

That is with the answer choices, my bad.