Question

How do you solve 8x + 6y = 4 and 3x + 5y = 28?

Answer 1

`(x,y) = (-74/11,106/11) = (6 8/11, 9 7/11)`

Explanation:

Given
[1]`color(white)("XXX")8x+6y=4`
[2]`color(white)("XXX")3x+5y=28`

Multiply [1] by 5 and [2] by 6 so we have two equations with the same coefficient for `y`
[3]`color(white)("XXX")40x+30=20`
[4]`color(white)("XXX")18x+30y=168`

Subtract [4] from [3]
[5]`color(white)("XXX")22x = -148`

Divide [5] by `22`
[6]`color(white)("XXX")x = -74/11`

Substituting `-74/11` for `x` in [2]
[7]`color(white)("XXX")3*(-74/11)+5y = 24`

Do some (tedious) arithmetic
[8]`color(white)("XXX")y= 106/11`