Question

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

2x + y = 1

4x + 2y = −2

Answer 1

You have:\[2x+y=1,\]\[4x+2y=-2.\]Solve for \(y\) in the first equation:\[y=1-2x,\]\[4x+2y=-2.\]Plug \(y\) from the first equation into the second equation and solve for \(x\):\[4x+2(1-2x)=-2.\]I assume you can do this step?

Answer 2

Okay, since this is a special case, I'll show you:\[4x+2(1-2x)=-2,\]\[\implies4x+2-4x=-2,\]\[\implies0=-4.\]Since we arrive at a contradiction, then we know that both lines must be parallel and that there is no solution for \(x\).