Two lines are represented by the equations 2x + 4y = 8 and x + 2y = 4. What can be concluded about this system?

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Question

Two lines are represented by the equations 2x + 4y = 8 and x + 2y = 4. What can be concluded about this system?

Accepted Answer

The system has infinitely many solutions because the equations represent the same line — Dividing the first equation by 2 gives x + 2y = 4, which is identical to the second equation. The two equations represent the same line, so every point on the line is a solution — infinitely many solutions exist.

Answer

The system has exactly one solution at (2, 1)

Answer

The system has infinitely many solutions because the equations represent the same line

Answer

The system has two solutions because there are two equations

Answer

The system has no solution because the lines are parallel

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