Question

How do you solve this system of equations: `y= - 6x - 13 and 7x + 2y = - 16`?

Answer 1

`(x,y)to(-2,-1)`

Explanation:

`y=-6x-13to(1)`

`7x+2y=-16to(2)`

`color(blue)"Substitute "y=-6x-13" into equation "(2)`

`rArr7x+2(-6x-13)=-16`

`rArr7x-12x-26=-16`

`rArr-5x-26=-16`

`"add 26 to both sides"`

`-5xcancel(-26)cancel(+26)=-16+26`

`rArr-5x=10`

`"divide both sides by "-5`

`(cancel(-5) x)/cancel(-5)=10/(-5)`

`rArrx=-2`

`color(blue)"substitute "" this value into equation "(1)`

`rArry=(-6xx-2)-13=12-13=-1`

`"the point of intersection "=(-2,-1)`
graph{(y+6x+13)(y+7/2x+8)((x+2)^2+(y+1)^2-0.04)=0 [-10, 10, -5, 5]}