Solve the simultaneous equations: x^2 + y^2 = 10 and x + 2y = 5
1.)x2 + y2 = 10 2.)x + 2y = 5. Rearrange 2nd equation: x = 5 - 2y. Substitute back into 1st equation: (5 - 2y)2 + y2 = 10. Multiply out brackets: 4y2 - 20y + 25 + y2 = 10. Rearrange equation: 5y2 - 20y + 15 = 0. Simplify equation: y2 - 4y + 3 = 0. Factorise: (y-3)(y-1) = 0. Therefore: y = 3 or y = 1. Sub values of y back into equation 2 to find x values. When y = 3: x + 2(3) = 5, so x + 6 =5, therefore x = -1 and so the coordinates are (-1, 3). When y = 1: x + 2(1) = 5, so x + 2 = 5, therefore x = 3 and so coordinates are (3, 1). To check sub x and y values into equations and see if you get the correct answers
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