Solve the following simultaneous equations: x^2 + 2y = 9, and y = x + 3.

Label the two equations as the following: x² + 2y = 9 y = x + 3 Equation 2 can be substituted into equation 1, giving: x² + 2( x + 3 ) = 9Expanding the brackets and subtracting 9 from both sides means equation 1 becomes x² + 2x - 3 = 0Then we can factorise this to create (x + 3)(x - 1) = 0Which means x = -3, and x = 1.
Substituting these values into equation 2 gives usy = 0 and y = 4, respectively.So the solutions are (-3, 0) and (1, 4).