alleryStart learning →Solve the system by graphing: y = 2x - 3 and -6x + 3y = -9.
AExactly one solution, at the point (3, 3)
BInfinitely many solutions, since the lines coincide
CNo solution, since the lines are parallel
DNo solution, since the lines never touch
Answer & Solution
Correct answer: B. Infinitely many solutions, since the lines coincide
1. Rewrite the second equation in slope-intercept form: -6x + 3y = -9 becomes 3y equals 6x minus 9, then y equals 2x minus 3.
2. Compare the two lines: both have slope 2 and y-intercept -3, so they are the same line.
3. Since every point on one line also lies on the other, the system has infinitely many solutions.
_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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