1. Solving Systems of Equations Using Elimination
Conncections - Thursday, November 11
Unit D.5
Solving Systems of Equations Using Elimination
Students will be able to solve systems of equations using elimination
Unit D.5 - Solving Systems Using Elimination

2. Solving Systems - Elimination
Another way to solve systems of equations is with the elimination method.
With elimination, you get rid of (eliminate)one of the variables by adding or subtracting equations.
The elimination method is sometimes called the addition and subtraction
method.
FHS
Systems of Equations

3. Using Elimination - Example 1
Use elimination to solve the system of equations.
Step 1: Find the value of one variable.
3x + 2y = 4
The y-terms have opposite coefficients.
4x – 2y = -18
7x = -14
Add the equations to eliminate y.
x = -2
First part of the solution.
FHS
Systems of Equations

4. Example 1 (cont.)
Step 2: Substitute the x-value into one of the original equations to solve for y.
3(-2) + 2y = 4
Substitute -2 in for x.
2y = 10
y = 5
Second part of the solution.
The solution is the ordered pair (-2, 5).
FHS
Systems of Equations

5. What if Elimination Does Not Work?
When you cannot eliminate one of the variables by just adding or subtracting the two equations, it is still possible to solve the system.
Sometimes you can multiply one or both of the equations by some number that would make elimination possible.
FHS
Systems of Equations

6. Conncections - Thursday, November 11
Unit D.5
Example 2 - Using Elimination
Use elimination to solve the system of equations.
Step 1: To eliminate x, multiply both sides of the first equation by 2 and both sides of the second equation by –3.
2(3x + 5y) = 2(–16)
–3(2x + 3y) = –3(–9)
6x + 10y = –32
–6x – 9y = 27
Add the equations. →
First part of the solution:
y = –5
FHS
Systems of Equations
Unit D.5 - Solving Systems Using Elimination

7. Conncections - Thursday, November 11
Unit D.5
Example 2 (Cont.)
Step 2: Substitute the y-value into one of the original equations to solve for x.
3x + 5(–5) = –16
3x – 25 = –16
3x = 9
x = 3
Second part of the solution
The solution for the system is (3, –5).
FHS
Systems of Equations
Unit D.5 - Solving Systems Using Elimination