Question

How do solve the following linear system?: `3x – 4y = 7, x-y=2`?

Answer 1

`(x,y)=(+1,-1)`

Explanation:

Given
[1]`color(white)("XXX")3x-4y=7`
[2]`color(white)("XXX")x-y=2`

There are several ways to solve this but since it was asked under "Systems Using Substitution", we will approach it that way:

Rearrange [2] into an equation in terms of `x`
[3]`color(white)("XXX")x=y+2`

Now substitute `(y+2)` for `x` in [1]
[4]`color(white)("XXX")3(y+2)-4y=7`

Expanding and simplifying [4]
[5]`color(white)("XXX")-y+6=7`
or
[6]`color(white)("XXX")y=-1`

Now substitute `(-1)` for `y` back in [2] (or you could have used [1])
[7]`color(white)("XXX")x-(-1)=2`
Simplifying:
[8]`color(white)("XXX")x=1`