Question

How do you solve using elimination of `2x+5y=17` and `6x-5y=-9`?

Answer 1

Add the equations to eliminate y and solve for x, and then substitute back to solve for y

Explanation:

Starting with
`{(2x + 5y = 17), (6x - 5y = -9):}`

We wish to solve for one of the variables by eliminating the other with addition or subtraction.
Note that we have `5y` in the first equation and `-5y` in the second. This means we may eliminate the variable `y` without further manipulation (in a more complicated case, we may need to first multiply both sides of one of the equations by a constant).
To do this, we can add the second equation to the first.

`(2x + 5y) + (6x - 5y) = 17 + (-9)=> 8x = 8`

Dividing both sides by 8 gives `x = 1`.

Then we simply substitute our result for `x` into either of the original equations. For example, using the first one gives
`2(1) + 5y = 17 => 5y = 15 => y = 3`

So the solution is `{(x = 1), (y=3):}`