Solve the system: x + y = 7 and x - y = 1.

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Multiple Choice

Solve the system: x + y = 7 and x - y = 1.

Explanation:
Eliminating a variable by adding the equations is a quick way to solve this kind of system. Add the two equations: (x + y) + (x − y) = 7 + 1, which gives 2x = 8, so x = 4. Then substitute x = 4 into the first equation: 4 + y = 7, yielding y = 3. The pair x = 4, y = 3 satisfies both equations since 4 + 3 = 7 and 4 − 3 = 1. The other option pairs don’t fit the second equation (for example, 3 and 4 give 3 − 4 = −1; 5 and 2 give 5 − 2 = 3; 2 and 5 give 2 − 5 = −3). So the correct solution is x = 4, y = 3.

Eliminating a variable by adding the equations is a quick way to solve this kind of system. Add the two equations: (x + y) + (x − y) = 7 + 1, which gives 2x = 8, so x = 4. Then substitute x = 4 into the first equation: 4 + y = 7, yielding y = 3. The pair x = 4, y = 3 satisfies both equations since 4 + 3 = 7 and 4 − 3 = 1. The other option pairs don’t fit the second equation (for example, 3 and 4 give 3 − 4 = −1; 5 and 2 give 5 − 2 = 3; 2 and 5 give 2 − 5 = −3). So the correct solution is x = 4, y = 3.

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