Question

How do you solve the following system of equations?: `4x – y = 14 , -3x + 3y=10`?

Answer 1

`(x,y)=(52/9,82/9)`
`color(white)("XXXXXXXXXXXX")`(not all answers are pretty)

Explanation:

Solving by Substitution
Given
[1]`color(white)("XXX")4x-y=14`
[2]`color(white)("XXX")-3x+3y=10`

Re-write [1] as
[3]`color(white)("XXX")y= 4x-14`

Substitute `4x-14` (from [3]) for `y` in [2]
[4]`color(white)("XXX")-3x+3(4x-14)=10`

Simplify
[5]`color(white)("XXX")9x-42=10`

[6]`color(white)("XXX")9x=52`

[7]`color(white)("XXX")x=52/9`

Substituting `(52/9)` for `x` in [1]
[8]`color(white)("XXX")4xx(52/9)-y=14`

[9]`color(white)("XXX")y= 208/9-14 = (208-126)/9 = 82/9`