Difficult Passport to Advanced Math Problem with Solution Today I would like to provide a solution for the SAT math problem I posted on Friday. Level 5 Passport to Advanced Math y = x2 + 5x + 6 7x + 4 – y = 0 How many solutions are there to the system of equations above of the form (x,y), with x a real number? (A) 0 (B) 1 (C) 2 (D) More than 2 * Solution by substitution: We solve the second equation for y by adding y to each side of the equation: 7x + 4 = y We now replace y by 7x + 4 in the first equation to get 7x + 4 = x2 + 5x + 6 We now add –7x – 4 to each side of the equation to get 0 = x2 – 2x + 2 The equation x2 – 2x + 2 = 0 has discriminant b2 – 4ac = (–2)2 – 4 ⋅ 1 ⋅ 2 = 4 – 8 = –4 Since the discriminant is negative, there are no real values of x that satisfy the equation. So, the answer is choice A. Notes: (1) To learn more about the discriminant of a quadratic equation, see the following post: The Discriminant of a Quadratic Equation (2) For one method of solving quadratic equations, see the following post: The Quadratic Formula Share this problem with your Facebook friends that are preparing for the SAT If you’re preparing for the SAT, you may want to check out the Get 800 collection of SAT math books. Comments comments