Solve the linear system 2x + y = 7 and x − y = 1; find (x, y).

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Multiple Choice

Solve the linear system 2x + y = 7 and x − y = 1; find (x, y).

Explanation:
Solving a linear system means finding the pair (x, y) that makes both equations true, i.e., where the two lines intersect. Use substitution: from the second equation, x = y + 1. Plug this into the first equation: 2(y + 1) + y = 7, which simplifies to 3y + 2 = 7, so y = 5/3. Then x = y + 1 = 5/3 + 1 = 8/3. Check: 2x + y = 2*(8/3) + 5/3 = 16/3 + 5/3 = 21/3 = 7, and x − y = 8/3 − 5/3 = 3/3 = 1, so both equations hold. Therefore the solution is (8/3, 5/3). The other given pairs don’t satisfy both equations when checked.

Solving a linear system means finding the pair (x, y) that makes both equations true, i.e., where the two lines intersect. Use substitution: from the second equation, x = y + 1. Plug this into the first equation: 2(y + 1) + y = 7, which simplifies to 3y + 2 = 7, so y = 5/3. Then x = y + 1 = 5/3 + 1 = 8/3.

Check: 2x + y = 2*(8/3) + 5/3 = 16/3 + 5/3 = 21/3 = 7, and x − y = 8/3 − 5/3 = 3/3 = 1, so both equations hold. Therefore the solution is (8/3, 5/3). The other given pairs don’t satisfy both equations when checked.

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