# How do you solve the system #x-5y=10# and #-2x+10y=-20# by graphing?

##### 1 Answer

Draw a straight line through an arbitrary pair of solution points for for each equation. Normally where the lines intersect will be the solution.

(Fails in this case; see below)

#### Explanation:

For the equation:

a simple pair of solution points would be the x and y intercepts:

We can plot those points and draw a line through them:

graph{(x-5y-10)(x^2+(y+2)^2-0.05)((x-10)^2+y^2-0.05)=0 [-4.96, 15.04, -5.12, 4.88]}

Then we can do the same thing for:

However, as we can see, the intercepts are identical for both equations,

and therefore the lines will be identical.

There is no single solution; any solution for one equation will also be a solution for the other.