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The 6 steps to solving a 2-variable equation:

5a + 2b = 3
4a + 5b = 6

1) Find a on its own:
a = (3-2b)/5
2) Substitute into the other equation:
4((3-2b)/5) + 5b = 6
3) Multiply (only if there are fractions):
4(3-2b) + 25b = 30
4) Distribute:
12 - 8b + 25b = 30
5) Combining like terms:
17b = 18
6) Divide
b = 18/17

AND YOU'RE DONE!!! :D