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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 sharply down from left to right.
    • The line passes through the following points:
      • (0 comma 8)
      • (3 comma 4)
      • (5 comma four thirds)
  • For the second line in the system:
    • The line slants gradually up from left to right.
    • The line passes through the following points:
      • (0 comma 1)
      • (3 comma 4)
      • (5 comma 6)

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

A.

(2,3 )

B.

3,4

C.

(4,5 )

D.

(5,6 )

For the first line in the system: The line slants sharply 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. If a point x,y lies on both lines in the graph of a system of two linear equations, the ordered pair x,y is a solution to the system. The graph shown is the graph of a system of two linear equations, where the two lines in the graph intersect at the point 3,4. Therefore, the point 3,4 lies on both lines, so the ordered pair 3,4 is the solution to the system.

Choice A is incorrect. The point 2,3 lies on one, not both, of the lines in the graph shown.

Choice C is incorrect. The point 4,5 lies on one, not both, of the lines in the graph shown.

Choice D is incorrect. The point 5,6 lies on one, not both, of the lines in the graph shown.

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