Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.
Solve a system by elimination after deciding whether a multiplier is needed
Problem
Solve the system by elimination, multiplying one equation first if needed: \(2x~+~y~=~9\), \(x~-~y~=~3\).
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What this problem is really about
Before multiplying either equation, inspect the coefficient pairs to see whether cancellation is already available. We’ll compare their magnitudes and signs, scale only if necessary, and combine complete equations with the matching operation on both sides. Solving the surviving variable, back-substituting, and checking both rows will verify both the chosen elimination setup and the solution.
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