Question

How do solve the following linear system?: `x+2y=1 , 4 x+ 16y = 2`?

Answer 1

`(x,y) = (3/2, -1/4)`

Explanation:

Given
[1]`color(white)("XXX")x+2y=1`
[2]`color(white)("XXX")4x+16y=2`

Multiply [1] by `4` to generate the same `x` coefficient as in [2]
[3]`color(white)("XXX")4x+8y=4`

Subtract [3] from [2]
[4]`color(white)("XXX")8y=-2`

Divide both sides of [4] by `8`
[5]`color(white)("XXX")y = -1/4`

Substitute `(-1/4)` for `y` in [2]
[6]`color(white)("XXX")4x+16*(-1/4)=2`

Simplify:
[7]`color(white)("XXX")4x-4 = 2`

Add `4` to both sides
[8]`color(white)("XXX")4x = 6`

Divide both sides of [8] by `4`
[9]`color(white)("XXX")x=3/2`