Integrated Math 1 / Unit 6: Systems of Equations and Inequalities
6.2 Substitution
Notes
In substitution, solve one equation for a variable, then substitute that expression into the other equation.
- Use it when a variable is already isolated or has coefficient 1.
- Solve the one-variable equation, then substitute back to find the other variable.
- Example: $y = 3x$ and $x + y = 12$: $x + 3x = 12$, so $x = 3$ and $y = 9$.
- Write the answer as an ordered pair $(x, y)$.
Practice
Solve: $y = 3x$ and $x + y = 12$.
$x + 3x = 12$ gives $x = 3$, and $y = 3(3) = 9$.
Solve: $x = 2y - 1$ and $3x + y = 11$.
$3(2y - 1) + y = 11 \Rightarrow 7y = 14 \Rightarrow y = 2$. Then $x = 3$.
Solve: $y = -x + 6$ and $y = 2x - 3$.
$-x + 6 = 2x - 3$ gives $3x = 9$, so $x = 3$ and $y = 3$.
Ready for more? Take the Unit 6 test.