Question

How do you solve the system y = -3x + 6 and 3x-y = 6?

Answer 1

`x=2`
`y=0`

Explanation:

The equations are

1. `y=-3x+6`
2. `3x-y=6`

Solve the value of `x` by substitution

`3x-y=6`
`3x-(-3x+6)=6`, plug in the value of y
`3x+3x-6=6`, simplify and combine like terms
`6x=12`, isolate x
`(cancel6x)/cancel6=12/6`
`x=2`

To find the value of `y`, where

`y=-3x+6`, plug in the value of x
`y=-3(2)+6`, simplify
`y=-6+6`
`y=0`

Checking:

1. `y=-3x+6`
   `0=-3(2)+6`
   `0=-6+6`
   `0=0`

2. `3x-y=6`
   `3(2)-0=6`
   `6-0=6`
   `6=6`