Solve the system: x - y = 4 and x + y = 8.

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Multiple Choice

Solve the system: x - y = 4 and x + y = 8.

Explanation:
To solve this pair of linear equations, use elimination by adding the equations. When you add them, the y terms cancel: (x − y) + (x + y) = 4 + 8, which simplifies to 2x = 12. So x = 6. Then substitute x = 6 into x + y = 8: 6 + y = 8, giving y = 2. The pair (6, 2) satisfies both equations since 6 − 2 = 4 and 6 + 2 = 8. Other listed pairs don’t satisfy both equations (for example, (4, 4) gives 0 for the first equation, not 4; (2, 6) gives −4 for the first; (8, 0) gives 8 for the first).

To solve this pair of linear equations, use elimination by adding the equations. When you add them, the y terms cancel: (x − y) + (x + y) = 4 + 8, which simplifies to 2x = 12. So x = 6. Then substitute x = 6 into x + y = 8: 6 + y = 8, giving y = 2. The pair (6, 2) satisfies both equations since 6 − 2 = 4 and 6 + 2 = 8. Other listed pairs don’t satisfy both equations (for example, (4, 4) gives 0 for the first equation, not 4; (2, 6) gives −4 for the first; (8, 0) gives 8 for the first).

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