Question

How do you solve the system of equations `-x-5y=1` and `-3x+7y=25` by combination?

Answer 1

x = -6, y = 1

Explanation:

Multiply the 1st equation by -3, and add to the second. This combines the two equations, and allows you to eliminate one of the unknown variables, and therefore easily solve for the other.

So, you'd have:

`3x + 15y = -3`
`+ (-3x + 7y = 25)`

giving:

`22y = 22` so therefore `y = 1`.

Feed this back into either of the original equations to solve for the remaining unknown variable x:

`-x - 5 = 1`

add 5 to both sides of the above eq.:

`-x = 6`

`x = -6`

as a sanity check, feed your solutions back into the original equations to see if they are correct:

`-3(-6) + 7(1) = 18 + 7 = 25` check!
`-(-6) -5(1) = 1` check!

GOOD LUCK!