Question

How do you solve `x + 4y = 19` and `y = -2x - 4`?

Answer 1

`(x,y)to(-5,6)`

Explanation:

`x+4y=19to(1)`

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

`"substitute "y=-2x-4" into equation "(1)`

`x+4(-2x-4)=19larrcolor(blue)"distribute"`

`rArrx-8x-16=19`

`rArr-7x-16=19`

`"add 16 to both sides"`

`rArr-7x=19+16=35`

`"divide both sides by "-7`

`rArrx=35/(-7)=-5`

`"substitute "x=-5" into equation "(2)`

`rArry=(-2xx-5)-4=10-4=6`

`"the point of intersection of the 2 equations "=(-5,6)`
graph{(y+1/4x-19/4)(y+2x+4)=0 [-20, 20, -10, 10]}