Question

How do you solve `6x - 2y = -16` and `4x + 4y = -32`?

Answer 1

`x=-4`
`y=-4`-

Explanation:

`6x-2y=-16` and
`4x+4y=-32`
or
`2x+2y=-16`
or
`x+y=-8`
Adding up the equations `6x-2y=-16` and `2x+2y=-16`
We get
`6x-2y+2x+2y=-16-16`
or
`8x=-32`
or
`x=-32/8`
or
`x=-4`--------------------Ans `1`
By putting the value `x=-4` in the equation `x+y=-8`
We get
`-4+y=-8`
or
`y=4-8`
or
`y=-4`-----------------------Ans `2`

Answer 2

`x = -4 and y = -4`

Explanation:

Neither of the equations is in the simplest form. Let's do that first and see what we end up with.

`6x-2y = -16 " "(div 2)" " rArr 3x-y =-8 ..........A`

`4x + 4y = -32 " " (div 4) " " rArr x+y =-8 ............B`

We notice that `+y and -y` are additive inverses which will add to 0 if we add equations `A and B` together.

`color(white)(................)3x-y =-8 ..........A`
`color(white)(.................)x+y =-8 ............B`

`A+B color(white)(.........) 4x = -16`
`color(white)(.....................)x = -4`
`color(white)(....................)y = -4`