Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.
Solve a system by elimination after multiplying both equations
Problem
Solve \(2x~+~3y~=~13\) and \(3x~-~2y~=~0\) by elimination. State the multipliers applied to the first and second equations and the resulting ordered-pair solution.
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What this problem is really about
When neither coefficient pair cancels, use a common multiple to create opposites efficiently. We’ll determine one multiplier for each equation, apply it to every variable term and constant, and add the scaled rows to eliminate the targeted variable. Back-substitution and two original-equation checks then verify the multipliers as well as the ordered-pair solution.
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