Solve the simultaneous equations: y = x - 2 and y^2 + x^2 = 10

y = x - 2

y² + x² = 10

1. Subsitutute the top equation into the second equation:

     (x-2)² + x² = 10

2. Expand out the brackets and simplify:

     x² - 4x + 4 + x² = 10

     2x² - 4x - 6 = 0

     x² - 2x - 3 = 0

3. Factorise the quadratic equation to find the two values of x:

    (x - 3) (x + 1) = 0

    x = 3, x = -1