Given 6x+2y=4 and 5x+y=8, solve the simultaneous equations to find x and y.

The key here is to eliminate one of the variables; it doesn't matter whether we start by trying to get rid of x or y we will arrive at the same solution. For us to eliminate either x or y it is easiest to find a way of making the co-efficient (number before the x or y) the same in both equations by multiplying through by a number as follows. 

If we take 5x+y=8 and multiply through by 2 (don't forget to multiply both sides), we get


So we now have 10x+2y=16 and 6x+2y=4

We can rearrange both equations to give 2y=10x-16=6x-4.

We have now eliminated y leaving us with 10x-16=6x-4

Rearranging gives 10x-6x=16-4   so 4x=12. Therefore x=3. 

If we substitute this back into one of our original equations such as 5x+y=8, we get 15+y=8.

So y=8-15=-7

Therefore, x=3 and y=-7. 

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