Solve the system: 2x - y = 3 and x + y = 1.

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Multiple Choice

Solve the system: 2x - y = 3 and x + y = 1.

Explanation:
Elimination is a clear way to handle this system because the y terms cancel when you combine the equations. Add 2x − y = 3 and x + y = 1: the y’s cancel, leaving 3x = 4, so x = 4/3. Then substitute x = 4/3 into x + y = 1: 4/3 + y = 1, giving y = -1/3. The solution is (4/3, -1/3). Quick check: in the first equation, 2x − y = 2*(4/3) − (−1/3) = 8/3 + 1/3 = 3; in the second, x + y = 4/3 − 1/3 = 1.

Elimination is a clear way to handle this system because the y terms cancel when you combine the equations. Add 2x − y = 3 and x + y = 1: the y’s cancel, leaving 3x = 4, so x = 4/3. Then substitute x = 4/3 into x + y = 1: 4/3 + y = 1, giving y = -1/3. The solution is (4/3, -1/3). Quick check: in the first equation, 2x − y = 2*(4/3) − (−1/3) = 8/3 + 1/3 = 3; in the second, x + y = 4/3 − 1/3 = 1.

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