Question

How do solve the following linear system?: `4x+y=6 , x-4y=-24`?

Answer 1

`(x,y)=(0,6)`

Explanation:

Given:
[1]`color(white)("XXX")4x+y=6`
[2]`color(white)("XXX")x-4y=-24`

Re-write [1] as
[3]`color(white)("XXX")y=6-4x`

Substitute `(6-4x)` for `y` in [2]
[4]`color(white)("XXX")x-4(6-4x)=-24`

Simplify [4]
[5]`color(white)("XXX")xcancel(-24)+4x=cancel(-24)`

[6]`color(white)("XXX")5x=0`

[7]`color(white)("XXX")x=0`

Substitute `0` for `x` in [1]
[8]`color(white)("XXX")4(0)+y=6`

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