Solve the system of equations: 2x + 3y = 5 and x - y = 1. What are 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 of equations: 2x + 3y = 5 and x - y = 1. What are x and y?

Explanation:
When solving a system of linear equations, you’re looking for the pair (x, y) that makes both equations true at the same time. A handy way is substitution: solve one equation for one variable, then substitute into the other. From the second equation, x = y + 1. Substitute into the first: 2(y + 1) + 3y = 5, which simplifies to 5y + 2 = 5, so y = 3/5. Then x = y + 1 = 3/5 + 1 = 8/5. Check: 2(8/5) + 3(3/5) = 16/5 + 9/5 = 25/5 = 5, and 8/5 − 3/5 = 5/5 = 1, so both equations hold. The solution is x = 8/5 and y = 3/5.

When solving a system of linear equations, you’re looking for the pair (x, y) that makes both equations true at the same time. A handy way is substitution: solve one equation for one variable, then substitute into the other.

From the second equation, x = y + 1. Substitute into the first: 2(y + 1) + 3y = 5, which simplifies to 5y + 2 = 5, so y = 3/5. Then x = y + 1 = 3/5 + 1 = 8/5.

Check: 2(8/5) + 3(3/5) = 16/5 + 9/5 = 25/5 = 5, and 8/5 − 3/5 = 5/5 = 1, so both equations hold. The solution is x = 8/5 and y = 3/5.

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