Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.
Solve a system with fractions or decimals
Problem
Solve the system with fractions or decimals: \(0.5x~+~y~=~7\), \(x~-~y~=~2\).
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What this problem is really about
Decimal coefficients do not change the logic of elimination. We’ll inspect the coefficient signs for immediate cancellation, add matching terms while combining the decimal coefficients exactly, and solve the remaining one-variable equation. Back-substitution and checks in both originals will confirm the ordered-pair solution.
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