If x + y = 7 and x - y = 1, what is x?

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Multiple Choice

If x + y = 7 and x - y = 1, what is x?

Explanation:
You can solve this by eliminating one variable. Add the two equations: (x + y) + (x − y) = 7 + 1. The y terms cancel, leaving 2x = 8, so x = 4. Then y = 7 − x = 3, and check: x − y = 4 − 3 = 1, which matches. If you try other values, you’ll find they don’t satisfy the second equation after solving for y; for example, x = 3 would give y = 4 and x − y = −1, x = 5 would give y = 2 and x − y = 3, etc. So the only solution is x = 4.

You can solve this by eliminating one variable. Add the two equations: (x + y) + (x − y) = 7 + 1. The y terms cancel, leaving 2x = 8, so x = 4. Then y = 7 − x = 3, and check: x − y = 4 − 3 = 1, which matches.

If you try other values, you’ll find they don’t satisfy the second equation after solving for y; for example, x = 3 would give y = 4 and x − y = −1, x = 5 would give y = 2 and x − y = 3, etc. So the only solution is x = 4.

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