Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.
Solve a system by elimination when coefficients already cancel
Problem
Solve the system by elimination with matching opposite coefficients: \(2x~+~y~=~7\), \(x~-~y~=~2\).
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What this problem is really about
Elimination is immediate when one variable already has opposite coefficients. We’ll align the equations, add each matching column and both constants, and solve the one-variable equation left after cancellation. Substituting that value into an original row recovers the other coordinate, while a final check in both equations confirms that no sign error entered the ordered pair.
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