Question

How do you solve y= -2x + 2 and 6x + 2y = 3?

Answer 1

`(x,y)=(-1/2,3)`

Explanation:

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

The form given for equation [1] makes solution by substitution the most obvious method:

Base on [1] we can substitute `(-2x+2)` for `y` in [2]
[3]`color(white)("XXX")6x+2(-2x+2)=3`

Simplifying [3]
[4]`color(white)("XXX")2x+4=3`
or
[5]`color(white)("XXX")x=-1/2`

We can now substitute `(-1/2)` for `x` in [1]
[6]`color(white)("XXX")y=-2(-1/2)+2=3`