Question

How do solve the following linear system?: `3/2x - 3y = -9/4 , 2/3x + 4y = -1`?

Answer 1

`(x,y)=(-3/2,0)`

Explanation:

Given:
[1]`color(white)("XXX")3/2x-3y=-9/4`
[2]`color(white)("XXX")2/3x+4y=-1`
To make the solution easier we will clear the fractions by
multiplying [1] by `4` and [2] by `3` to get
[3]`color(white)("XXX")6x-12y=-9`
[4]`color(white)("XXX")2x+12y=-3`

Adding equations [3] and [4] gives
[5]`color(white)("XXX")8x=-12`
and after dividing by `8`
[6]`color(white)("XXX")x=-3/2`

Substituting `(-3/2)` (from [6]) for `x` in [2]
[7]`color(white)("XXX")2/3xx(-3/2)+4y=-1`
Simplifying
[8]`color(white)("XXX")y=0`

Graphically:
graph{(3/2x-3y+9/4)(2/3x+4y+1)=0 [-5.07, 2.725, -1.414, 2.483]}