Solve the system of equations: x + y = 5 and x - y = 1.

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Multiple Choice

Solve the system of equations: x + y = 5 and x - y = 1.

Explanation:
Solving a pair of linear equations uses elimination to remove a variable. Add the equations to cancel y: x + y plus x − y equals 5 plus 1, which gives 2x = 6, so x = 3. Substitute x = 3 into x + y = 5 to get 3 + y = 5, so y = 2. The pair (3, 2) satisfies both equations, meaning those two lines cross at that point. If you test another option, like (2, 3), it makes the second equation false (2 − 3 ≠ 1), so it doesn’t fit both equations.

Solving a pair of linear equations uses elimination to remove a variable. Add the equations to cancel y: x + y plus x − y equals 5 plus 1, which gives 2x = 6, so x = 3. Substitute x = 3 into x + y = 5 to get 3 + y = 5, so y = 2. The pair (3, 2) satisfies both equations, meaning those two lines cross at that point. If you test another option, like (2, 3), it makes the second equation false (2 − 3 ≠ 1), so it doesn’t fit both equations.

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