Question x-8-y-

2.3 Systems Involving Nonlinear Equations - Line + parabola intersections
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x = 8

y = x 2 + 8

The graphs of the equations in the given system of equations intersect at the point x,y in the xy-plane. What is the value of y ?

A.

8

B.

24

C.

64

D.

72

x = 8 y = x 2 + 8 The graphs of the equations in the

Medium-difficulty · SAT Math · Systems Involving Nonlinear Equations — Line + parabola intersections. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice D is correct. Since the graphs of the equations in the given system intersect at the point x,y, the point x,y represents a solution to the given system of equations. The first equation of the given system of equations states that x = 8 . Substituting 8 for x in the second equation of the given system of equations yields y=82+8, or y = 72 . Therefore, the value of y is 72 .

Choice A is incorrect. This is the value of x , not y .

Choice B is incorrect and may result from conceptual or calculation errors.

Choice C is incorrect and may result from conceptual or calculation errors.