Question

How do you solve the system of equations `-3x + 2y = 19` ad `x - 6y = - 1`?

Answer 1

`(x,y)to(-7,-1)`

Explanation:

`-3x+2y=19to(1)`

`x-6y=-1to(2)`

`"from equation "(2)color(white)(x)x=6y-1to(3)`

`"substitute "x=6y-1" in equation "(1)`

`-3(6y-1)+2y=19`

`-18y+3+2y=19`

`-16y+3=19`

`"subtract 3 from both sides"`

`-16y=16`

`"divide both sides by "-16`

`y=16/(-16)=-1`

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

`x=-6-1=-7`

`"point of intersection "=(-7,-1)`
graph{(y-3/2x-19/2)(y-1/6x-1/6)=0 [-10, 10, -5, 5]}

Answer 2

`x=-7,y=-1`

Explanation:

Multiplying the second equation by `3` and adding to the first we get

`-16y=16` so `y=-1`

substituing this in the second equation
`x+6=-1`
so
`x=-7`