Question for-th
- For the first line in the system:
- The line slants sharply down from left to right.
- The line passes through the following points:
- (4 comma 1)
- (StartFraction 32 Over 7 EndFraction 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:
- (StartFraction 32 Over 9 EndFraction comma 0)
- (4 comma 1)
The graph of a system of linear equations is shown. The solution to the system is . What is the value of ?
For the first line in the system: The line slants sharply down from left to right.
Medium-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
The correct answer is . A solution to a system of equations must satisfy each equation in the system. It follows that if is a solution to the system, the point lies on the graph in the xy-plane of each equation in the system. According to the graph, the point that lies on the graph of each equation in the system is . Therefore, the solution to the system is . It follows that the value of is .
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