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.
Related questions
A rule counting sign changes to bound the number of positive real zeros belongs to:A single point where a rational graph is undefined, shown by an open circle, is a hole or A horizontal line that a graph approaches as inputs grow without bound is a horizontal:A vertical line that a graph rushes towards but never crosses is a vertical:A polynomial with real coefficients has 2 plus 3i as a zero, so it must also have as a zerFor a rational zero, numerators come from factors of the constant term and denominators frA polynomial takes a negative value at 3 and a positive value at 4, so between them it musA graph crosses straight through the x-axis at a zero. That zero has multiplicity that is: