If x^2 + y^2 = 20 and y=10 - 2x, find x and y.
First work out y2 using the second equation, making sure to do this using the FOIL technique. Then substitute this into the first equation to get 5x2 - 40x - 80 = 0. All the terms in this can be divided by 5 to get x2 - 8x +16=0. Then factorise this to get (x-4)2=0. Therefore, x=4. Putting this value of x into the second equation gets the result of y=2
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