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

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

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

Explanation:
When solving a two-equation linear system, you can use elimination to cancel a variable. Add the two equations to eliminate y: (x + y) + (2x − y) = 7 + 1, which gives 3x = 8, so x = 8/3. Next, plug x back into one equation to find y. Using x + y = 7: 8/3 + y = 7, so y = 7 − 8/3 = 13/3. So the solution is x = 8/3 and y = 13/3. You can verify: x + y = 8/3 + 13/3 = 21/3 = 7, and 2x − y = 16/3 − 13/3 = 3/3 = 1. The given options don’t match this solution, so none of them are correct for this system.

When solving a two-equation linear system, you can use elimination to cancel a variable. Add the two equations to eliminate y: (x + y) + (2x − y) = 7 + 1, which gives 3x = 8, so x = 8/3.

Next, plug x back into one equation to find y. Using x + y = 7: 8/3 + y = 7, so y = 7 − 8/3 = 13/3.

So the solution is x = 8/3 and y = 13/3. You can verify: x + y = 8/3 + 13/3 = 21/3 = 7, and 2x − y = 16/3 − 13/3 = 3/3 = 1. The given options don’t match this solution, so none of them are correct for this system.

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