Question

Which equation, when graphed with the given equation, will form a system that has no solution?

Oy=4x+12
O y=-4x
O y=-12
y=-4(X+3)

Answer 1

The answer is y = 4x + 12

The thing that makes it a solution is that it crosses with the given system y= -4(X+3)

This point evaluates to y= -4x -12
The system exactly opposite to this is y= 4x +12.

When they have an opposite slope they can never cross. These points have different slopes.

I have also sent a picture of the systems graphed to give a visual.