Question

How do you solve the following system: #4x+3y= -1 , 4x-5y-23=0 #?

Answer 1

`x=-5/32 and y = -1/8`

Explanation:

The `x` terms are the same in both equations.

If you subtract the two equations the `x` terms will be eliminated.

`color(white)(xxxxxxx) 4x+3y =-1" "...A`
`color(white)(xxxxxxx) 4x-5y =" "0" "...B`

`A-B:color(white)(xxxxxx)8y = -1`
`color(white)(xxxxxxxxxxxx)y = -1/8`

`color(white)(xxx) 4x +3(-1/8) = -1`

`color(white)(xxxxxxxx) 4x -3/8 = -1`
`color(white)(xxxxxxxxxxx) 4x = -1+3/8`
`color(white)(xxxxxxxxxxx) 4x = -5/8`
`color(white)(xxxxxxxxxxxx) x = -5/32`

Check in `B`

`4(-5/32) -5(-1/8)`

`-5/8 +5/8`

`=0`

Answer 2

`x=2` and `y=-3`

Explanation:

`(4x+3y)-(4x-5y)=-1-23`

`8y=-24`, so `y=(-24)/8=-3`

Hence,

`4x+3*(-3)=-1`

`4x-9=-1`

`4x=8`, thus `x=8/4=2`