How do you solve simultaneous equations?

Simultaneous equations can be simple or complicated to solve, but once you recognise the pattern required they are quite straightforward. 

For instance, If 3x+y=14 and y-2x=-1 what are the values of x and y?

In this question you can see that both equations have one common variable which is 'y', therefore if we make both equations equal y we can substitute make them equal each other and then solve for one variable - the 'x'. Then we can substitute the value of x into the original equation to solve for 'y'.

eg. 14-3x=y and y=2x-1 therefore 14-3x=2x-1 therefore 14+1=2x+3x therefore 15=5x therefore x=3

once we substitute this back into the original equation - 3*3+y=14 so 9+y=14 therefore y=5

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