1. Section 8.2 Solving Linear Systems by Elimination
Pre-calculus 11
Chapter 8.2

2. I) Solving Linear Systems By Elimination
Goal: Add or subtract the equations so that you will cancel out one variable
Find the LCM for the coefficients for ‘x’
Multiply each equation so that the coefficients of ‘x’ become the LCM
Add/subtract the equations to cancel out one variable
Solve
Plug the answer back into the original equation and solve for the 2nd variable

3. EX: SOLVE THE SYSTEM BY ADDITION/SUBTRACTION
1. Coefficients of “x”
2. LCM: 12
3. Subtract the equations
4. Solve for the remaining variable
5. Plug into original equation to solve for 2nd variable

4. PRACTICE: SOLVE BY ADDITION/SUBTRACTION
1. Coefficients of “y”
2. LCM: 12
3. Subtract the equations
4. Solve for the remaining variable
5. Plug into original equation to solve for 2nd variable

5. PRACTICE: SOLVE BY ADDITION/SUBTRACTION
Multiply all terms by LCD to cancel out your denominators
Coefficients of “x”
Add the equations

6. Properties of Linear Systems:
Multiplying an entire equation by a constant does not change the solution
Adding or subtracting two equations does not change the solution
Slope and Y-intercept
are still the same

7. Solving Systems Involving Quadratics
Eliminate one of the variables by adding/subtracting the two equations
After the two equations are combined, factor or use the quadratic formula to solve the equation
Use this answer to solve the other variable
The solution to this system is

8. Practice: Solve this system by elimination
Solve for “y”
The solution to this system is

9. Homework:
P317 #5(aced), 7, 8, 14 – 17a (18**)