Solve the system of equations. y = 3x + 2 y = x^2 – 4x + 2 a. (0, –2) and (–7, –23) b. (–7, –23) and (0, 2) c. (–7, 23) and (0, –2) d. (0, 2) and (7, 23)

When you solve a system of equations you are determining where the curves intersect in a coordinate plane.  These places of intersection share the exact same x and y points.  Since both equations above are already solved for y, and since the y values for each will be the same, let's set them equal to each other and solve for x.  .  The way to solve for x is to combine like terms, set the resulting polynomial equal to 0, and factor to find x.  Doing that gives us .  We can factor a common x out of those terms to get 0 = x(x-7).  By the Zero Product Property theorem, x = 0 or x-7 = 0.  So x = 0 and x = 7.  Sub those x values back in to solve for y.  y = 3(0)+2 and y = 2.  So one of our coordinates is (0, 2).  y = 3(7)+2 so y = 23.  The other coordinate is (7, 23).  Those choices are found together in D above.