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Solve the system by graphing: y = (1/2)x - 3 and x - 2y = 4.
ANo solution, since the lines are parallel
BOne solution, at the point (2, -2)
CInfinitely many solutions, since the lines coincide
DNo solution, since the lines are perpendicular
Answer & Solution
Correct answer: A. No solution, since the lines are parallel
1. Rewrite the second equation in slope-intercept form: x - 2y = 4 becomes y equals one-half x minus 2.
2. Compare the two lines: the first has slope one-half and y-intercept -3, and the second has slope one-half and y-intercept -2.
3. The slopes are equal but the y-intercepts differ, so the lines are parallel and never meet.
4. Since no point lies on both lines, the system has no solution.
_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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