Solve for x and y: 2x + y = 7 and x - y = 1.

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Multiple Choice

Solve for x and y: 2x + y = 7 and x - y = 1.

Explanation:
Solving a pair of linear equations by substitution. Express one variable from one equation and substitute into the other to find the value of the other variable, then back-substitute. From the second equation, y = x − 1. Plugging into the first equation gives 2x + (x − 1) = 7, which simplifies to 3x − 1 = 7, so x = 8/3. Then y = x − 1 = 8/3 − 1 = 5/3. This pair satisfies both equations: 2x + y = 16/3 + 5/3 = 7 and x − y = 8/3 − 5/3 = 1. Other options don’t satisfy both equations (for example, x = 3, y = 1 makes the second equation 3 − 1 = 2, not 1; x = 2, y = 3 gives 2 − 3 = −1).

Solving a pair of linear equations by substitution. Express one variable from one equation and substitute into the other to find the value of the other variable, then back-substitute.

From the second equation, y = x − 1. Plugging into the first equation gives 2x + (x − 1) = 7, which simplifies to 3x − 1 = 7, so x = 8/3. Then y = x − 1 = 8/3 − 1 = 5/3. This pair satisfies both equations: 2x + y = 16/3 + 5/3 = 7 and x − y = 8/3 − 5/3 = 1.

Other options don’t satisfy both equations (for example, x = 3, y = 1 makes the second equation 3 − 1 = 2, not 1; x = 2, y = 3 gives 2 − 3 = −1).

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