Solve x + y = 5 and x − y = 1
The unique solution is x = 3, y = 2.
Problem
Answer
Step-by-step solution
Step 1: Add
Adding cancels y: 2x = 6.
Step 2: Solve for x
x = 3.
Step 3: Back-substitute
3 + y = 5, so y = 2.
Why this works
Two linear equations in two unknowns describe two lines. A nonzero determinant means they intersect once. Adding is elimination; substitution (solve one equation for y, plug into the other) produces the same pair.
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