How do you solve simultaneous equations?

To solve simultaneous equations you need to cancel out variables like x and y one at a time to solve for the other. In the edexcel GCSE 2017 paper this question came up: solve simultaneously x²+y²=25 y-3x=13
From this you can see it's easier to work with the second equation first. You can move this around to make y=3x+13, then substitute this into the first equation to get: x²+(3x+13)²=25. You should then expand this bracket out and find x²+9x²+39x+39x+169=25 and condense this to 10x²+78x+144=0. It can then be divided by 2 to get 5x²+39x+72=0
This then needs to be factorised as: (x+3)(5x+24)=0. You then must set each individual bracket equal to 0 and obtain x=-3 and x=-24/5. Now you have found these you can easily substitute them into our y=3x+13 equation and find that y=3(-3)+13 which gives y=4 and y=3(-24/5)+13 which gives y=-7/5SOLVED