Question

How do you solve this system of equations: `-8x - y = 14 and - 5x + y = 12`?

Answer 1

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

Explanation:

Equation 1: `-8x-y=14`
Equation 2: `-5x+y=12`

To solve these equation try to remove one variable.

equation 1 +equation 2
`-8x-y-5x+y=14+12`
`=>-13x=26`
`=>x=-2`

Substitute value of `x` in any of equation.
Substituting value of `x` in equation 2

`-5(-2)+y=12`
`=>10+y=12`
`=>y=2`

Answer 2

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

Explanation:

`-8x-y=14to(1)`

`-5x+y=12to(2)`

`"using the "color(blue)"substitution method"`

`"from "(2)" express y in terms of x"`

`rArry=12+5xto(3)`

`color(blue)"substitute "y=12+5x" into "(1)`

`-8x-(12+5x)=14`

`rArr-8x-12-5x=14`

`rArr-13x-12=14`

`"add 12 to both sides"`

`-13xcancel(-12)cancel(+12)=14+12`

`rArr-13x=26`

`"divide both sides by - 13"`

`(cancel(-13) x)/cancel(-13)=26/(-13)`

`rArrx=-2`

`"substitute this value into "(3)`

`rArry=12+(5xx-2)=12-10=2`

`rArr"point of intersection "=(-2,2)`
graph{(y-5x-12)(y+8x+14)((x+2)^2+(y-2)^2-0.04)=0 [-10, 10, -5, 5]}