Question bank / Systems of two linear equations in two variables

Math · AlgebraMedium

6x−4y=106x - 4y = 10
3x−2y=53x - 2y = 5
How many solutions does the system of equations above have?

A

Zero

B

Exactly one

C

Exactly two

D

Infinitely many

Show answer and explanation

Answer: D

Multiplying the second equation by 2 gives 6x−4y=106x - 4y = 10, which is identical to the first equation. The two equations describe the same line, so there are infinitely many solutions.

Choice A would be correct only if the lines were parallel with different intercepts, but here the constants also match.

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