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

Apr 7, 2016

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: $x - 5 y = 10$
a simple pair of solution points would be the x and y intercepts:
$\textcolor{w h i t e}{\text{XXX}} \left(x , y\right) = \left(0 , - 2\right)$ and $\left(x , y\right) = \left(10 , 0\right)$
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: $- 2 x + 10 y = - 20$
color(white)("XXX")(x,y)=0,2) and $\left(x , y\right) = \left(10 , 0\right)$
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.