Solve the following simultaneous equations: 2x + 2y = 14; 4x - 2y = 10

By Elimination:
We can add the equations together because +2y and -2y will cancel out: 2x + 4x = 14 + 10
This gives 6x = 24, so x = 4
We can put x back into one of the simultaneous equations: 2(4) + 2y = 14
Therefore, 2y = 6 so y = 3
We can check our answers in the other equation: 4(4) - 2(3) = 10
By Substitution:
We can rearrange the first equation to put y on the left hand side of the equation: 2y = 14 - 2x, so: y = 7 - x
We can substitute this third equation into the second equation: 4x - 2(7 - x) = 10 and 4x - 14 - (-2x) = 10
By collecting like terms on each side:
6x = 24, therefore x = 4
We now substitute x = 4 into one of the first equations to get y = 3