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2.3 Systems Involving Nonlinear Equations - Line + parabola intersections
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  • For the curve in the system:
    • Moving from left to right:
      • The curve passes from quadrant 2 to quadrant 1.
      • In quadrant 2, the curve trends up gradually to point (0 comma 3.25).
      • In quadrant 1, the curve trends up sharply.
    • The curve passes through the following points:
      • (1 comma 3.5)
      • (2 comma 4)
      • (4 comma 7)
  • For the line in the system:
    • The line slants gradually up from left to right.
    • The line passes through the following points:
      • (2 comma 4)
      • (7 comma 7.5)

The graph of a system of a linear equation and a nonlinear equation is shown. What is the solution x,y to this system?

A.

0,0

B.

0,2

C.

2,4

D.

4,0

For the curve in the system: Moving from left to right: The curve passes from quadrant

Easy-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 C is correct. The solution to the system of two equations corresponds to the point where the graphs of the equations intersect. The graphs of the linear equation and the nonlinear equation shown intersect at the point 2,4. Thus, the solution to the system is 2,4.

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

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

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

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