Question

Using the diagram, explain why y =2x+1 and y=2x-3 have no solutions.

Answer 1

Because they have the same inclination so if we try to draw them on a diagram they will be parallel to each other.

Answer 2

The solutions to an equation are the coordinates of the points that belong to both lines.
The points where the graphs meet belongs to both lines and are solutions to the system of equations.
In our case the lines have the same slope therefore are parallel, so they will never meet so they will have to points that are common to both lines in the same time, so the system of equations given has no solutions.