Question

Question #745a3

Answer 1

`x=-5`
`y=-6`
For the step by step explanation, see below

Explanation:

First off we want to make it so that we can eliminate one of the variables after adding the equations together. The x variables have the same coefficient, so it would be easiest to deal with them first. Both are negative though, so to eliminate them they must be opposite sides. So let's multiply the bottom equation by -1.

`-x-y=11`
`-(-x+3y=-13) = x-3y=13`

So now we can add the equations together. It's easiest to see this when the equations are right on top of each other:

`-x-y=11`
`+x-3y=13`

Take `-x` and add it to `x` to eliminate the variable (or get 0). Now we have to add the other variable, or add `-y` to `-3y`, which we get `-4y` from. Finally we add the numbers at the end of each equation, or `11+13 = 24`

After this we gather one full equation with only one variable remaining:

`-4y=24`

Solve for y by dividing each side by -4.

`y=-6`

Now that we know this we can find `x` by plugging the `y` value into any of the starting equations. So let's do the first one:

`-x-(-6)=11`
`-x=5`
`x=-5`

The final part is optional, but it's to check by plugging in your new values for `x` and `y` into the other equation (that you didn't use).
So:

`-(-5)+3(-6) = -13`
`5-18=-13`
`-13=-13`

Hope that helps!

Answer 2

`x=-5`, `y=-6`

Explanation:

Strategy: Pick one of the two equations. It doesn't matter which one. Rewrite it so that you have `x` alone on one side. Then plug it into the other equation to find the solution to `y`. Finally, take your solution for `y` and find your solution for `x`.

Step 1. Pick one of the two equations.
`-x-y=11`

Step 2. Rewrite it so that you have `x` alone on one side.
Add `y` to both sides
`-x=11+y`

Multiply both sides by `-1`
`x=-11-y`

Step 3. Plug the expression in step into the other equation and solve
`-color(red)(x)+3y=-13`
`-(color(red)(-11-y))+3y=-13` replace `x`
`11+y+3y=-13` multiply the negative through
`11+4y=-13` combining like terms
`4y=-24` subtract `11` from both sides
`y=-6` divide both sides by `4`

Step 4. Plug this solution for `y` into step one above
`x=-11-color(red)(y)`
`x=-11-(color(red)(-6))`
`x=-11+6`
`x=-5`