Question

How do you solve the system of equations `8x + 3y = - 4` and `5x + 2y = 6`?

Answer 1

`(x,y)=(-26,68)`

Explanation:

I'll solve this by first eliminating the `y` terms in both equations:

`E1: 8x+3y=-4=>16x+6y=-color(white)(1)8`
`E2: 5x+2y=color(white)(-)6=>ul(15x+6y=color(white)(-)18`
`E1-E2: color(white)(8x+3y=0.00)x+0y=-26`

`:. color(blue)(x=-26)`

Substitute back into one one of the original equations:

`E1: 8(-26)+3y=-4`

`E1: -208+3y=-4`

`E1: 3y=204=>color(blue)(y=68)`

Let's check our answer via graphing (because the lines are so close to being parallel, I've had to really focus the graph):

graph{(8x+3y+4)(5x+2y-6)=0[-27,-25,66,70]}