Solve the system: 2x + 3y = 7 and x - y = 1.

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Multiple Choice

Solve the system: 2x + 3y = 7 and x - y = 1.

Explanation:
Solving a pair of linear equations by substitution: take one equation to express a variable in terms of the other, then substitute into the other equation. From x − y = 1, we get x = y + 1. Plug that into 2x + 3y = 7: 2(y + 1) + 3y = 7, which simplifies to 2y + 2 + 3y = 7, so 5y + 2 = 7 and y = 1. Then x = y + 1 = 2. The pair (2, 1) satisfies both equations: 2·2 + 3·1 = 4 + 3 = 7 and 2 − 1 = 1. Quick check of other listed options shows they don’t meet both equations (for example, (1, 2) gives 2·1 + 3·2 = 8, not 7).

Solving a pair of linear equations by substitution: take one equation to express a variable in terms of the other, then substitute into the other equation. From x − y = 1, we get x = y + 1. Plug that into 2x + 3y = 7: 2(y + 1) + 3y = 7, which simplifies to 2y + 2 + 3y = 7, so 5y + 2 = 7 and y = 1. Then x = y + 1 = 2. The pair (2, 1) satisfies both equations: 2·2 + 3·1 = 4 + 3 = 7 and 2 − 1 = 1. Quick check of other listed options shows they don’t meet both equations (for example, (1, 2) gives 2·1 + 3·2 = 8, not 7).

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