Math: e9349667

ID: e9349667

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Advanced Math)

Comment: There is nothing unusual about this system of equations.

Method 1: I do not typically substitute when presented a system of equations because I see more students make errors using substitution than elimination. That said, it is easy to substitute for y in the second equation, since the first tells us exactly what y equals in terms of x.

x + y + 1 = 0

x + (x^2 + 2x + 1) + 1 = 0

x^2 + 3x + 2 = 0

(x + 2)(x + 1) = 0

x = -2 or -1

Never mind the quadratic. If x = -2 in the equation above, then y = 1; if x = -1, y = 0. Thus, the sum of the two possible y-values is 1 + 0, or 1. The correct answer is (D).

Method 2: This is another seemingly hand-picked question for Desmos. Graph the two equations to look for the points of intersection, then add the two y-values at those points.

1 + 0 is 1, and the correct answer is (D).

Method 3: As I touched on earlier, in method 1, you could just as easily eliminate to solve. Isolate y in the second equation, then eliminate as you would with two linear equations.

y = x^2 + 2x + 1

y = -x - 1

0 = x^2 + 3x + 2

0 = (x + 2)(x + 1)

x = -2 or -1

y = -(-2) - 1 --> 1 or y = -(-1) - 1 --> 0

1 + 0 = 1

The correct answer is (D).