10x + 7y=1

-5x-7y=24

Okay, so since both y values share the same number, let's add both equations so the y values cancel out leaving us to solve for x.

10x + (-5x) = 5x

7y + (-7y) = 0

1+24=25

Now we have 5x=25

divide both sides by 5 and we have x=5

Now that we know x=5, we can plug it into one of the problems to find y.

Let's do 10 (5) + 7y=1

50+7y=1 subtract 5 and we get 7y=-49

divide - 7 from both sides and we get y=-7

so there you have it x=5 and y=-7