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2.3 Systems Involving Nonlinear Equations - Substitution/elimination with nonlinear components
0:00

  • For the absolute value function in the system:
    • Moving from left to right:
      • The function slants sharply down to the point (negative 3 comma 4).
      • The function then slants sharply up.
    • The function passes through the following points:
      • (negative seven halves comma nine halves)
      • (negative 3 comma 4)
      • (negative five halves comma nine halves)
  • For the linear function in the system:
    • The function slants sharply up from left to right.
    • The function passes through the following points:
      • (negative seven halves comma nine halves)
      • (0 comma 8)

The graph of a system of an absolute value function and a linear function is shown. What is the solution x,y to this system of two equations?

A.

-72,92

B.

-3,4

C.

72,92

D.

0,8

For the absolute value function in the system: Moving from left to right: The function slants

Medium-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 C is correct. The solution to a system of two equations corresponds to the point where the graphs of the equations intersect. The graphs of the linear function and the absolute value function shown intersect at a point with an x-coordinate between - 4 and - 3 and a y-coordinate between 4 and 5 . Of the given choices, only -72,92 has an x-coordinate between - 4 and - 3 and a y-coordinate between 4 and 5 .

Choice A is incorrect. This is the y-intercept of the graph of the linear function.

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

Choice D is incorrect. This is the vertex of the graph of the absolute value function.

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