Solve the simultaneous equations. x^2 + y^2 = 29. y-x = 3

The 2 equations are: 1) x² + y² = 29 2) y-x=3 In this kind of simultaneous equation, you cannot take it away from each other. Instead, you need to substitue. To do so, rearrange the 2nd equation to make x or y the subject. To make y the subject, we add x on each side: y= 3+ x We can now substitute y into the first equation and solve it. x² + y² = 29 x² + (3+ x)(3+ x) = 29 x² + x² + 6x + 9 =29 2x² + 6x -20 = 0 x² + 3x -10 = 0 (x-2)(x+5) = 0 So x can be: x-2 = 0   or   x+5 = 0 x = 2             x = -5 This means y can be: y-x = 3 so y = 3 + x When x = 2, y = 3+2 = 5. When x = -5, y = 3+(-5) = -2.