How do you solve the system of equations #y=-x-8# and #y=2/5x-1# by graphing?

1 Answer
Tom M.
Dec 10, 2017

#(-3, -5)#

To solve simultaneous equations graphically, we plot both graphs, and find the coordinates that they intercept.

Explanation:

So lets do this.

To plot each straight line (and these are straight line graphs, there are no powers of x besides #x^1#) we need to find two points they pass through. It's easy to take the points of which the lines cross the coordinate axes.

Take #y=-x-8#

#"Let "x=0, y=-8#
#"Let "y=0#
#-x-8=0#
#x=-8#
So line passes through #(0, -8)# and #(-8,0)#.

We can plot this line.

graph{-x-8-y=0 [-21.23, 19.3, -12.6, 7.67]}

Now for the other line:

Take #y=2/5x-1#
#"Let "x=0, y=-1#
#"Let "y=0#
#0=2/5x-1#
#1=2/5x#
#x=5/2#
So the line passes through #(0, -1)# and #(5/2, 0)#

We draw this line on the same axes.

graph{(-x-8-y)(2/5x-1-y)=0 [-21.23, 19.3, -12.6, 7.67]}

The solution to these simultaneous equations will be where the lines cross. This is at the point #(-5, -3)#

so #x=-5# and #y=-3#

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