Question

How do you solve the system of equations: 5m + 2n = -8 ; 4m + 3n = 2?

Answer 1

`(m,n) = (-4,6)`

Explanation:

[1]`color(white)("XXXX")5m+2n=-8`
[2]`color(white)("XXXX")4m+3n = 2`

Multiply [1] by 3, then [2] by 2, generating two equations with the same coefficient for `n`
[3}`color(white)("XXXX")15m+6n= -24`
[4]`color(white)("XXXX")8m+6n=4`

Subtract [4] from [3]
[5]`color(white)("XXXX")7m = -28`

Divide both sides by 7
[6]`color(white)("XXXX")m = -4`

Substitute `(-4)` for `m` in [1]
[7]`color(white)("XXXX")5(-4)+2n = -8`

Simplify
[8]`color(white)("XXXX")2n = 12`

Divide by 2
[9]`color(white)("XXXX")n = 6`