Question

How do you solve by substitution `0.3x-0.2y=0.5` and `x-2y= -5`?

Answer 1

By simplifying and re-arranging the terms, we get
`(x,y) = (5,5)`

Explanation:

[1]`color(white)("XXXX")` `0.3x-0.2y=0.5`
[2]`color(white)("XXXX")` `x-2y = -5`

I would suggest the first thing to do is to simplify [1] by multiplying everything by 10
[3]`color(white)("XXXX")` `3x-2y =5`

In order to use substitution, re-arrange [2] to isolate `x`
[3]`color(white)("XXXX")` `x = 2y-5`

Substitute `2y-5` for `x` in [3]
[4]`color(white)("XXXX")` `3(2y-5) -2y = 5`
Simplify
[5]`color(white)("XXXX")` `4y -15 = 5`
[6]`color(white)("XXXX")` `y = 5`

Using [6], substitute `5` for `y` in [2]
[7]`color(white)("XXXX")` `x-2(5) = -5`
[8]`color(white)("XXXX")` `x=5`