Solve the system: 2x + y = 7 and x - y = 1. Find x and y.

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Multiple Choice

Solve the system: 2x + y = 7 and x - y = 1. Find x and y.

Explanation:
When solving a system of linear equations, you can use elimination to remove one variable and solve for the other. Here, adding the two equations cancels y: (2x + y) + (x − y) = 7 + 1, which gives 3x = 8, so x = 8/3. Then use one equation to find y. From x − y = 1, y = x − 1 = 8/3 − 1 = 5/3. Checking both equations confirms the solution: 2x + y = 2*(8/3) + 5/3 = 16/3 + 5/3 = 7, and x − y = 8/3 − 5/3 = 1. The pair is x = 8/3 and y = 5/3.

When solving a system of linear equations, you can use elimination to remove one variable and solve for the other. Here, adding the two equations cancels y: (2x + y) + (x − y) = 7 + 1, which gives 3x = 8, so x = 8/3. Then use one equation to find y. From x − y = 1, y = x − 1 = 8/3 − 1 = 5/3. Checking both equations confirms the solution: 2x + y = 2*(8/3) + 5/3 = 16/3 + 5/3 = 7, and x − y = 8/3 − 5/3 = 1. The pair is x = 8/3 and y = 5/3.

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