Solve the system: 3x - y = 7 and x + y = 5. Find x and y.

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Multiple Choice

Solve the system: 3x - y = 7 and x + y = 5. Find x and y.

Explanation:
Elimination is a quick way to handle a system when adding the equations cancels one variable. Here, strong cancellation happens with y when you add the two equations: (3x − y) + (x + y) = 7 + 5. The y’s cancel, giving 4x = 12, so x = 3. Plugging that into x + y = 5 yields 3 + y = 5, so y = 2. The pair (x, y) = (3, 2) satisfies both original equations: 3(3) − 2 = 7 and 3 + 2 = 5.

Elimination is a quick way to handle a system when adding the equations cancels one variable. Here, strong cancellation happens with y when you add the two equations: (3x − y) + (x + y) = 7 + 5. The y’s cancel, giving 4x = 12, so x = 3. Plugging that into x + y = 5 yields 3 + y = 5, so y = 2. The pair (x, y) = (3, 2) satisfies both original equations: 3(3) − 2 = 7 and 3 + 2 = 5.

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