How many solutions does this system of equations have?

\[2x + y = 1\]
\[4x + 2y = 2\]

A. None
B. Exactly one
C. Exactly two
D. Infinitely many

2 x + y = 1 4 x + 2 y = 2∣ : 2 2 x + y = 1 2 x + y = 1
both equations are identical ⇒ D

Answered by konrad509 | 2024-06-10

Given the equations 2x+y=1 and 4x+2y=2, if we divide the second equation by 2, we are left with 2x+y=1, which is the same equation as the first. This means that the lines over lap, and that there are infinite places where they "intercept" Final answer: D. Infinitely many

Answered by FirstSineOfMadness | 2024-06-24

The given system of equations has infinitely many solutions because both equations represent the same line when simplified. Therefore, every point on that line is a solution. The correct answer is D. Infinitely many.
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Answered by FirstSineOfMadness | 2024-10-01