Question

How do you solve -2x-9y=-25 and -4x-9y=-23?

Answer 1

I found:
`x=-1`
`y=3`

Explanation:

I would add together the two equations (in columns) after multiplying the first by `-1` to get:
`{(color(red)(2x+9y=25)),(-4x-9y=-23):}` add together:
`-2x+0=2`
`x=2/-2=-1`
Substitute into the first equation:
`2-9y=-25`
`-9y=-27`
`y=27/9=3`

Answer 2

`{(x=-1),(y=3):}`

Explanation:

Your system of equations looks like this

`{(-2x-9y = -25), (-4x-9y = -23) :}`

Multiply the first equation by `(-1)` to get

`-2x-9y = -25| * (-1)`

`2x + 9y = 25`

The system now looks like this

`{(2x+9y = 25), (-4x-9y = -23) :}`

Add the left-hand sides and the right-hand sides of the two equations seprately to get

`2x + color(red)(cancel(color(black)(9y))) - 4x - color(red)(cancel(color(black)(9y))) = 25 - 23`

`-2x = 2 implies x= 2/((-2)) = -1`

Take this value of `x` into one of the two equations to get the value of `y`

`-2 * (-1) - 9y = -25`

`2 - 9y = -25`

`-9y = -27 implies y = ((-27))/((-9)) = 3`

The solution set to this system of equations is `x = -1` and `y = 3`.