Question

How do solve the following linear system?: `9 x-6y =3 , -3x -8y = -9`?

Answer 1

`(x,y) = (13/15,4/5)`

Explanation:

Given
[equation 1]`color(white)("XXX")9x-6y=3`
[equation 2]`color(white)("XXX")-3x-8y=-9`

If we multiply [equation 2] by `3` then the coefficient of `x` will be of the same magnitude as in [equation 1]
[equation 3]`color(white)("XXX")-9x-24y=-27`

Adding [equation 1] and [equation 3]
[equation 4]`color(white)("XXX")-30y=-24`

Dividing [equation 4] by `(-30)` gives
[equation 5]`color(white)("XXX")y= 24/30 = 4/5`

Substituting `4/5` for `y` in [equation 1]
[equation 6]`color(white)("XXX")9x-6xx4/5 =3`

[equation 7]`color(white)("XXX")9x=3+24/5=39/5`

Dividing [equation 7] by `9` gives
[equation 8]`color(white)("XXX")x=39/45=13/15`