Question

How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent `y = 2/3x` and `y = - 1/3 x + 6`?

Answer 1

`(x,y)=(-6,-4)`
This is a consistent system of equations (since it has a single solution)

Explanation:

Given:
`color(white)("XXX")y=2/3x`
`color(white)("XXX")y=-1/3x+6`

Multiplying everything in both equations by `3`
`color(white)("XXX")3y=2x`
`color(white)("XXX")3y=-x+18`

Subtracting the second from the first:
`color(white)("XXX")0=3x+18`
`color(white)("XXX")rArr x=-6`

and since `3y=2x`
`color(white)("XXX")3y=-12`
`color(white)("XXX")rArr y=-4`