The equations x + y = 2 and 2x + 2y = 4 describe the same line. How many solutions are there?

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Multiple Choice

The equations x + y = 2 and 2x + 2y = 4 describe the same line. How many solutions are there?

Explanation:
Two equations that describe the same line mean there are infinitely many solutions. Here, the second equation is just 2 times the first one: multiplying x + y = 2 by 2 gives 2x + 2y = 4. So they describe the same line, and every point on that line satisfies both equations. A line has infinitely many points, so there are infinitely many solutions to the system.

Two equations that describe the same line mean there are infinitely many solutions. Here, the second equation is just 2 times the first one: multiplying x + y = 2 by 2 gives 2x + 2y = 4. So they describe the same line, and every point on that line satisfies both equations. A line has infinitely many points, so there are infinitely many solutions to the system.

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