Question

How do you solve the system of equations `-y=3-2x` and `y=2x-3`?

Answer 1

The solution set is all the points on the line `y=2x-3`

Explanation:

If we take the first equation in the system:

`-y=3-2x`

and multiply by `-1`, we get:

`(-1)-y=(-1)(3-2x)=y=2x-3`

which is what the second equation in the system is.

And so the solution to the system of equations is the same as the entire set of ordered pairs that lie along the line `y=2x-3`. Graphically, the solution set is:

graph{2x-3}

(the line continues in both directions to infinity)