Solve the system 2x + y = 7 and x - y = 1. What is x?

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Multiple Choice

Solve the system 2x + y = 7 and x - y = 1. What is x?

Explanation:
Solving a system of two linear equations by substitution starts by expressing one variable in terms of the other from one equation, then plugging that expression into the other equation to solve for the remaining variable. From the second equation, x − y = 1 gives y = x − 1. Substitute this into the first equation: 2x + (x − 1) = 7. This simplifies to 3x − 1 = 7, so 3x = 8 and x = 8/3. To verify, find y = x − 1 = 8/3 − 1 = 5/3, and check both equations: 2x + y = 2*(8/3) + 5/3 = 16/3 + 5/3 = 21/3 = 7, and x − y = 8/3 − 5/3 = 1. The value x = 8/3 satisfies both equations, so that’s the solution.

Solving a system of two linear equations by substitution starts by expressing one variable in terms of the other from one equation, then plugging that expression into the other equation to solve for the remaining variable. From the second equation, x − y = 1 gives y = x − 1. Substitute this into the first equation: 2x + (x − 1) = 7. This simplifies to 3x − 1 = 7, so 3x = 8 and x = 8/3. To verify, find y = x − 1 = 8/3 − 1 = 5/3, and check both equations: 2x + y = 2*(8/3) + 5/3 = 16/3 + 5/3 = 21/3 = 7, and x − y = 8/3 − 5/3 = 1. The value x = 8/3 satisfies both equations, so that’s the solution.

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