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What is a solution of a system of two linear equations?
AAny ordered pair that makes one of the equations true
BThe y-intercept shared by both equations
CThe point where either line crosses the x-axis
DAn ordered pair (x, y) that makes both equations true
Answer & Solution
Correct answer: D. An ordered pair (x, y) that makes both equations true
1. The definition requires the ordered pair to make all of the equations in the system true at once, not just one of them.
2. Making only one equation true is not enough; the pair must satisfy every equation in the system to count as a solution.
3. A shared y-intercept or an x-intercept of just one line is a different, unrelated idea from a solution of the whole system.
_Source: OpenStax Elementary Algebra (CC BY 4.0), Ch 5 "Systems of Linear Equations", section 5.1 Solve Systems of Equations by Graphing_
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