Question

How do you solve the system of equations: y = -3x + 5 and 5x - 4y = -3?

Answer 1

`(x,y) = (1,2)`

Explanation:

[1]`color(white)("XXXX")` `y=-3x+5`
[2]`color(white)("XXXX")` `5x-4y=-3`

Since [1] gives us an expression for `y` in terms of `x`
the obvious solution method would be to substitute this expression for `y` in [2]
[3]`color(white)("XXXX")`5x-4(-3x+5)=-3#

Simplifying the left side
[4]`color(white)("XXXX")` `17x-20 = -3`

Adding 20 to both sides:
[5]`color(white)("XXXX")` `17x = 17`

Dividing by 17
[6]`color(white)("XXXX")` `x=1`

Substituting `1` for `x` back in [1]
[7]`color(white)("XXXX")` `y = -3(1)+5`

Simplifying
[8]`color(white)("XXXX")` `y=2`