I can try to explain this in a way you can understand.
The variable that stands alone, that doesn't have a number attached to it, is the one you must solve for. So taking the first equation, you need to move the 2X to the other side of the equal symbol by subtracting it from both sides, effectively making is -Y=3-2X. Then you need to make the Y positive in order to solve for Y, you divide the entire equation by -1, as it is assumed that the negative in front of the Y is 1.
With that, you plug the entire right side of the equal sign in for Y in the second equation, so it would look like X+5(-3+2X)=7. Then you first multiply 5 by -3 and then by 2X. Combine the X and the result from multiplying 5x10X. Simply add 15 to both side of the equal sign to move it to the right side of the equation. Then divide the whole equation by the number in front of X and you have solved for X.
...I hope that made some sort of sense.
[OOC: And I hope that is actually correct. THIS IS THE ONE THING IN MATHEMATICS THAT I CAN DO. THOUGH IT'S BEEN YEARS SINCE I'VE HAD TO DO IT. >.>]