alleryStart learning →The two rules in a system turn out to describe the very same line. How many pairs of values solve the system?
AInfinitely many, since every point on it fits
BExactly one, where the line meets itself
CNone, because a line cannot cross itself
DExactly two, one at each end of the line
Answer & Solution
Correct answer: A. Infinitely many, since every point on it fits
1. A solution is a point lying on both lines.
2. If the two rules describe one line, then every point on that line lies on both of them.
3. A line holds endlessly many points, so there are endlessly many solutions.
4. Such a system is called dependent.
5. Option B treats the overlap as a single crossing, but the lines overlap everywhere rather than at one place.
_Source: OpenStax College Algebra (CC BY 4.0), Ch 7 "Systems of Equations and Inequalities", section 7.1 Systems of Linear Equations: Two Variables_
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