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

1 Answer
Apr 7, 2016

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: #x-5y=10#
a simple pair of solution points would be the x and y intercepts:
#color(white)("XXX")(x,y)=(0,-2)# and #(x,y)=(10,0)#
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: #-2x+10y=-20#
#color(white)("XXX")(x,y)=0,2)# and #(x,y)=(10,0)#
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.