Question

x+7y=-5
2x-3y=5

Answer 1

use the first expression to get x=-5-7y, then sub that in for x in the second equation:
2(-5-7y)-3y=5
-10-14y-3y=5
-17y=15
y=-(15/17), now we can do x:
x=-5-7y=-5-7(-15/17)=-5+(105/17)=(-85+105)/17
x=-(20/17)
NOTE: there are MANY ways to do this problem, this is just one.

Answer 2

Another way: multiply the first equation by -2 and add it to the second.
-2(x+7y=-5) =>-2x-14y=10
+(2x-3y=5)
=-17y=15
y=-15/17, same as before. now substitute that in for y in the first equation and you get your x.