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Question for-th

1.4 Systems of Two Linear Equations - Graphical solution of two lines
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  • For the first line in the system:
    • The line slants gradually down from left to right.
    • The line passes through the following points:
      • (0 comma 5)
      • (2 comma 4)
      • (10 comma 0)
  • For the second line in the system:
    • The line slants sharply up from left to right.
    • The line passes through the following points:
      • (0 comma 0)
      • (2 comma 4)
      • (5 comma 10)

The graph of a system of linear equations is shown. What is the solution x,y to the system?

A.

(0,5)

B.

(2,4)

C.

(5,10)

D.

(10,0)

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

Easy-difficulty · SAT Math · Systems of Two Linear Equations — Graphical solution of two lines. 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. A solution to a system of equations must be the solution to each equation in the system. It follows that if x,y is a solution to the system, the point x,y lies on the graph in the xy-plane of each equation in the system. The point that lies on each graph of the system of linear equations shown is their intersection point 2,4. Therefore, the solution to the system is 2,4.

Choice A is incorrect. The point 0,5 lies on one, but not both, of the graphs of the linear equations shown.

Choice C is incorrect. The point 5,10 lies on one, but not both, of the graphs of the linear equations shown.

Choice D is incorrect. The point 10,0 lies on one, but not both, of the graphs of the linear equations shown.

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