What are the steps in solving problems involving a system of linear equation?

For example, take these 2 equations:

2x+5y=25(eq 1) and 3x+4y=17(eq 2)

First, since none of the variables have the same coefficient,you try to make them have it. How? Easy. You multiply both equations by a number till you get it. To solve, you multiply the whole first equation by 3 and the whole second equation by 2 which yields:

6x+15y=75 and 6x+8y=34.

Then, you subtract the first equation from the second equation which yields:

7y=41 so y=41/7.

Now you substitute in any equation:2x+5(41/7)=25

After simplification, x=-15/7.

So there you go, x=-15/7 and y=41/7.