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. [tex]3x+2= x^{2} -4x+2[/tex]. 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 [tex] x^{2} -7x=0[/tex]. 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.
