Question for-th

2.3 Systems Involving Nonlinear Equations - Substitution/elimination with nonlinear components
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  • For the line in the system:
    • The line slants sharply down from left to right.
    • The line passes through the following points:
      • (negative 2 comma 6)
      • approximately (0 comma 3.8)
  • 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 down sharply to the point (negative 2 comma 6).
        • The curve then trends down gradually to the y axis.
      • In quadrant 1, the curve trends down gradually.
    • As x increases, the curve approaches the line y equals 5.
    • The curve passes through the following points:
      • (negative 3 comma 8)
      • (negative 2 comma 6)

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.

6,0

B.

-2,6

C.

0,-2

D.

0,0

For the line in the system: The line slants sharply down from left to right. The

Easy-difficulty · SAT Math · Systems Involving Nonlinear Equations — Substitution/elimination with nonlinear components. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice B is correct. The solution x,y to the system of two equations corresponds to the point where the graphs of the equations intersect in the xy-plane. The graphs of the linear equation and the nonlinear equation shown intersect at the point -2,6. Thus, the solution x,y to this system is -2,6.

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

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

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