Question

How do you solve x + y = -1 and 6x – 2y = 18?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the first equation for `x`:

`x + y = -1`

`x + y - color(red)(y) = -1 - color(red)(y)`

`x + 0 = -1 - y`

`x = -1 - y`

Step 2) Substitute `(-1 - y)` for `x` in the second equation and solve for `y`:

`6x - 2y = 18` becomes:

`6(-1 - y) - 2y = 18`

`(6 xx -1) - (6 xx y) - 2y = 18`

`-6 - 6y - 2y = 18`

`-6 + (-6 - 2)y = 18`

`-6 + (-8)y = 18`

`-6 - 8y = 18`

`-6 + color(red)(6) - 8y = 18 + color(red)(6)`

`0 - 8y = 24`

`-8y = 24`

`(-8y)/color(red)(-8) = 24/color(red)(-8)`

`(color(red)(cancel(color(black)(-8)))y)/cancel(color(red)(-8)) = -3`

`y = -3`

Step 3) Substitute `-3` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = -1 - y` becomes:

`x = -1 - (-3)`

`x = -1 + 3`

`x = 2`

The Solution Is:

`x = 2` and `y = -3`

or

`(2, -3)`

Answer 2

Solve algebraically or by graphing the equations.

`x = 2`
`y = -3`

Explanation:

1. `x + y = -1`
   `6x - 2y = 18`
2. `6x + 6y = -6`
   `6x - 2y = 18`
   Multiply each side of one or both equations by a constant so that one variable (in this case `x`) in both equations has the same coefficient (in this case `6`).
3. `6x + 6y = -6`
   `-(6x - 2y = 18)`
   Subtract the second equation from the first using the distributive property `[ a (b + c) = ab + ac]`.
4. `8y = -24`
   `y = -3`
   Simplify and solve for `y` by dividing both sides by `8`.
5. `x + (-3) = -1`
   Plug `-3` in for y in one or both equations (the answer should be the same).
6. `x = 2`
   Solve for `x` (add `3` to both sides).
7. `x = 2`
   `y = -3`
   State the answer as `x` and `y` values or as a coordinate `(2, -3)` when graphing the equations.