Algebra 1 / Unit 6: Systems of Equations and Inequalities
6.3 Solving by Elimination
Notes
Elimination adds or subtracts the equations to cancel a variable.
- Line up like terms. If the coefficients of one variable are opposites, add the equations.
- If not, multiply one or both equations first so a variable will cancel.
Example: $2x + y = 7$ and $3x - y = 8$. Adding gives $5x = 15$, so $x = 3$ and $y = 1$.
Practice
Solve: $x + y = 10$ and $x - y = 4$.
Add: $2x = 14$, so $x = 7$ and $y = 3$.
To eliminate $y$ from $2x + 3y = 8$ and $5x - y = 3$, multiply the second equation by:
$-y \cdot 3 = -3y$ cancels $+3y$ when you add.
Solve: $3x + 2y = 16$ and $x + 2y = 8$.
Subtract: $2x = 8$, so $x = 4$ and $y = 2$.
Ready for more? Take the Unit 6 test.