Solve the system: x + y = 7 and x − y = -1. What are x and y?

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Multiple Choice

Solve the system: x + y = 7 and x − y = -1. What are x and y?

Explanation:
Eliminate a variable by adding the equations. When you add (x + y) and (x − y), the y terms cancel and you get 2x = 6, so x = 3. Then plug x into x + y = 7: 3 + y = 7, which gives y = 4. Check: 3 − 4 = −1, which matches the second equation. So the solution is x = 3 and y = 4. Other pairs fail one of the equations—for example, (4, 3) makes the second equation 4 − 3 = 1, not −1; (2, 5) and (5, 2) also don’t satisfy both equations.

Eliminate a variable by adding the equations. When you add (x + y) and (x − y), the y terms cancel and you get 2x = 6, so x = 3. Then plug x into x + y = 7: 3 + y = 7, which gives y = 4. Check: 3 − 4 = −1, which matches the second equation. So the solution is x = 3 and y = 4. Other pairs fail one of the equations—for example, (4, 3) makes the second equation 4 − 3 = 1, not −1; (2, 5) and (5, 2) also don’t satisfy both equations.

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