Question

How do solve the following linear system?: `x + y = 2, y = 4x + 4`?

Answer 1

You could use the "Substitution Method" to get
`color(white)("XXX")(x,y)=(-2/5,12/5)`

Explanation:

Given:
[1]`color(white)("XXX")x+y=2`
[2]`color(white)("XXX")y=4x+4`

Substitute `4x+4` for `y` (from equation [2]) in equation [1]
[3]`color(white)("XXX")x+4x+4=2`

Simplify equation [3]
[4]`color(white)("XXX")5x=-2`

[5]`color(white)("XXX")x=-2/5`

Substitute `(-2/5)` for `x` (from equation [5]) in equation [1]
[6]`color(white)("XXX")(-2/5)+y=2`

Simplify
[7]`color(white)("XXX")y=12/5`