Solve the following system of equations and show all work. y = x2 + 3 y = x + 5,

x = -1 and x = 2 Let's take the two equations and solve: y = x^2 + 3 y = x + 5 Since we're looking for the point where the two equations are equal to each other, let's start by setting them equal to each other, getting x^2 + 3 = x + 5 Now solve for x. Start by rearranging into a quadratic equation. x^2 + 3 = x + 5 x^2 + 3 - x - 5 = 0 x^2 - x - 2 = 0 We now need to factor (x^2 - x - 2) and I don't know if you've learned the quadratic formula yet. So let's do it manually. We know that the product of the roots will be -2 and the sum will be -1. So what numbers when multiplied together get -2 and when added get -1? Thinking for a while indicates that the values -2 and 1 work quite nicely. So we have (x^2 - x - 2) = (x - 2)(x + 1) So the solution is x = -1 and x = 2 which will give you y values of 4 and 7 respectively.

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