Integrated Math 1 / Unit 6: Systems of Equations and Inequalities
6.3 Elimination
Notes
In elimination, add or subtract the equations to cancel a variable. You may first multiply an equation so that coefficients match or are opposites.
- Add if the coefficients of a variable are opposites; subtract if they are equal.
- Example: $x + y = 10$ and $x - y = 4$. Adding gives $2x = 14$, so $x = 7$ and $y = 3$.
- Multiply whole equations (every term), not just one term.
- Check your answer in both original equations.
Practice
Solve: $x + y = 10$ and $x - y = 4$.
Add the equations: $2x = 14$, so $x = 7$. Then $y = 3$.
Solve: $2x + 3y = 12$ and $4x - 3y = 6$.
Add: $6x = 18$ gives $x = 3$. Then $6 + 3y = 12$ gives $y = 2$.
For $3x + 2y = 7$ and $5x + 4y = 13$, which step lets you eliminate $y$ by adding?
$-2(3x + 2y) = -6x - 4y$, which cancels $4y$ when added to the second equation.
Ready for more? Take the Unit 6 test.