Algebra 1 / Unit 6: Systems of Equations and Inequalities
6.2 Solving by Substitution
Notes
Substitution works well when one equation already has a variable alone. 1. Solve one equation for a variable (if it isn't already). 2. Substitute that expression into the other equation and solve. 3. Substitute back to find the other variable. Example: $y = 3x$ and $x + y = 12$: $x + 3x = 12$, so $x = 3$ and $y = 9$.
Practice
Solve: $y = x - 4$ and $2x + y = 11$.
$2x + x - 4 = 11 \Rightarrow 3x = 15$.
Solve: $x = 2y$ and $3x - y = 25$.
$6y - y = 25 \Rightarrow y = 5$, then $x = 10$.
In $y = 7 - 2x$ and $4x + 3y = 19$, substituting gives:
Replace $y$ with $7 - 2x$, keeping the parentheses.
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