Solve systems of two linear equations exactly and approximately using algebraic and graphical methods.
Solve a system by substitution when one variable is already isolated
Problem
Solve the system by substitution: \(y~=~2x~+~1\), \(x~+~y~=~10\).
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What this problem is really about
One equation already gives a complete expression for a variable, making substitution the shortest route. We’ll replace that variable in the other equation with the entire equivalent expression, simplify to one variable, and then back-substitute for the second coordinate. Writing the result in x-then-y order and checking both originals prevents an incomplete or reversed pair.
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