What is the solution for these simultaneous equations: y = x² = and y = X + 2 ?

To solve these simultaneous equations, we can set the two equations equal to each other:

x² = x + 2

Now, we have a quadratic equation that we can solve by setting it equal to zero:

x² - x - 2 = 0

Now, we can factor this quadratic equation:

(x - 2)(x + 1) = 0

Setting each factor equal to zero gives us two possible solutions for x:

x = 2 or x = -1

Now that we have the values of x, we can substitute them back into one of the original equations to find the corresponding values of y. Let's use the equation y = x + 2:

For x = 2:
y = 2 + 2
y = 4

For x = -1:
y = -1 + 2
y = 1

Therefore, the solutions to the simultaneous equations are:
x = 2, y = 4
x = -1, y = 1