Question

How do you solve the system `x+y=2` and `x-y=4`?

Answer 1

The solution is `( 3, -1 )`

Explanation:

In this case the solution can be found by using the "elimination method". Looking at the two equations I see that you have `+y` in equation one and `-y` in equation two. By adding the two equations together I will "eliminate" the `y` variable and then I can solve for `x`.

`x + y = 2`
`x - y = 4`

Add the two equation together and get:

`2x = 6`

x = 3 Now substitute `3` for `x` in either equation and solve for `y`

`x + y = 2`
`3 + y = 2`
`y = - 1`
The solution is `(3 , -1 )`
Now you can, and should, verify that your answer is correct by substituting the solution in the second equation. If it works out, you have the correct answer.
`x - y = 4`
`3 - (-1) =4`
`4 = 4`