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2.3 Systems Involving Nonlinear Equations - Substitution/elimination with nonlinear components
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  • For the absolute value function:
    • Moving from left to right:
      • The function slants sharply down to the point (4 comma 2).
      • The function then slants sharply up.
    • The function passes through the following points:
      • (1 comma 5) 
      • (4 comma 2)
      • (6 comma 4)
  • For the linear function:
    • The function slants sharply up from left to right.
    • The function passes through the following points:
      • (0 comma 4)
      • (1 comma 5)

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.

-1,5

B.

0,4

C.

1,5

D.

4,2

For the absolute value function: Moving from left to right: The function slants sharply down to

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 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 function and the absolute value function shown intersect at the point 1,5. Thus, the solution to the system is 1,5.

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

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

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

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