AlgebraMedium
Solve x + y = 5 and x − y = 1
Solve a two-variable linear system by elimination and verify the ordered pair.
Method: Elimination
Step-by-step solution
- 1
Add the equations
The y and −y terms cancel.
- 2
Solve for x
Divide by 2 to obtain x=3.
- 3
Substitute back
Use x+y=5 to get y=2.
- 4
Verify both equations
The pair (3,2) makes both original equations true.
Final answer
Elimination works efficiently because the y coefficients are opposites.
Common mistake
Adding only one side of the equations or losing a sign produces an inconsistent pair.
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