PSAT Math Grid-Ins Question 2: Answer and Explanation

Question: 2

The equations above intersect at two points. What is the product of the y-coordinates of the two points of intersection?

Correct Answer: 32

Explanation:

32

The question asks for the product of the y-coordinates of the two points of intersection of a system of equations. Since both equations are set equal to the same value, set the right sides of the two equations equal to each other and solve for x. This gives 4x² - 6x + 4 = 2x + 4. Subtract 2x and 4 from both sides to set the equation equal to 0, so the equation becomes 4x² - 8x = 0. Divide both sides of the equation by 4 to get x² - 2x = 0. Factor x out of the equation to get x(x - 2) = 0. Therefore, the two possible values for x are x = 0 and x = 2. Plug both of these values into the second equation to find the corresponding y-values. If x = 0, then y = 2(0) + 4 = 4. If x = 2, then y = 2(2) + 4 = 8. The two points of intersection are (0, 4) and (2, 8). Therefore, the product of the two possible values of y is 4 × 8 = 32. The correct answer is 32.