Question

How do solve the following linear system?: `y = 5x - 7, x= y - 11 x`?

Answer 1

`(x,y)=color(blue)(""(-1,-12))`

Explanation:

Given:
[1]`color(white)("XXX")y=5x-7`
[2]`color(white)("XXX")x=y-11x`

Using [1] we see we can substitute `(5x-7)` for `y` in [2]
[3]`color(white)("XXX")x=(5x-7)-11x`

then simplifying
[4]`color(white)("XXX")x=-6x-7`

[5]`color(white)("XXX")7x=-7`

[6]`color(white)("XXX")x=-1`

Now we can substitute `(-1)` for `x` back in [1]
[7]`color(white)("XXX")y=5*(-1)-7`

[8]`color(white)("XXX")y=-12`