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This is a system of two linear equations:
x+2y=11
3x-4y=-17
One way to solve this system is to solve for x (or y) in the first equation and then plug it into the second equation to solve for the other variable, which then allows us to solve for our original variable.
(1) Take the first equation and solve for x: x=11-2y
(2) Plug this value into the second equation: 3x-4y=3(11-2y)-4y=33-10y=-17. We see that y=5.
(3) We now plug this into either equation to solve for x:
From (1): x=11-2y=11-2(5)=1
We get x=1 and y=5. It's also always a good idea to plug the numbers we found into our original two equations to verify they work.
Indeed, x+2y=1+2(5)=1+10=11, and
3x-4y=3(1)-4(5)=3-20=-17.
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