Question

How do you solve the system `-2x+y=8 and y=-3x-2`?

Answer 1

`x=-2,y=4`

Explanation:

Plugging the second equation

`y=-3x-2` in the first one:

`-3x-2x-2=8`
adding `2` on both sides and collexting like Terms

`-5x=10`

`x=-2` so `y=6-2=4`

Answer 2

`(x,y)to(-2,4)`

Explanation:

`-2x+y=8to(1)`

`y=-3x-2to(2)`

`"equation "(2)" expresses y in terms of "x`

`"substitute "y=-3x-2" into equation "(1)`

`-2x-3x-2=8`

`-5x-2=8`

`"add 2 to both sides"`

`-5x=8+2=10`

`"divide both sides by "-5`

`x=10/(-5)rArrx=-2`

`"substitute "x=-2" into equation "(2)`

`y=6-2=4`

`"the point of intersection "=(-2,4)`
graph{(y+3x+2)(y-2x-8)=0 [-10, 10, -5, 5]}