How many solutions does the system $y = 2x + 5$ and $4x - 2y = 6$ have?
AZero solutions
BExactly one solution
CExactly two solutions
DInfinitely many solutions
Answer & Solution
Correct answer: A. Zero solutions
Rewrite the second equation: $4x - 2y = 6 \Rightarrow y = 2x - 3$. Both equations have slope 2 but different y-intercepts (5 vs $-3$), so the lines are parallel and never intersect. Therefore the system has zero solutions.
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