Question

Solve the system of equations by substitution. What is the solution for x?

2x + y = 1
4x + 2y = −2

Answer 1

Take the first equation an solve for x

x=(1-y)/2.

Then substitute this x into the second equation and solve for y

2=-2

However, we run into a contradiction, and the system has no solutions.

Answer 2

2x + y = 1 => 2x = 1 - y

4x + 2y = −2 = 2(2x) + 2y = -2
substituting for 2x this becomes
2(1 - y) + 2y = -2
2 - 2y + 2y = -2
2 = -2
this is a contradiction, so this system of equations does not have a solution