1. Solving Systems of Equation Using Elimination

3. Another method for solving systems of equations Eliminate one of the variables by adding the two equations together ELIMINATION

4. When to use this method: _________________________________ _________________________________ Systems of equations can have one of the following: One SolutionNo SolutionInfinitely Many Solutions Use when both equations are in standard form.

5. How will we eliminate???? Making opposites What’s the opposite of the following? 1)-4 2)3 3)-x 4)6y 4 -3 x -6y

6. Example 1:4x + 3y = 14x + 3y = 1 -2x – 3y = 1-2x – 3y = 1 Step 1 – Identify opposite pairs or make opposite pairs using multiplication. Step 2 – Add the two equations together and solve for the remaining variable. Step 3 – Find the other coordinate by substituting the value from step 2 into either of the original equations. Solution – The ordered pair, (x,y), using the values in step 2 and 3. Solution _________

7. Why we can do this: Remember that an equation stays balanced if you add equal amounts to both sides. Since 4x + 3y = 1, you can add 4x + 3y to one side of an equation and 1 to the other side and the balance is maintained. -2x – 3y = 1 + (4x + 3y)+(1)

8. Example 2: 2x + y = 3Example 3: -x + 2y = 12 -2x + 5y = -9 x + 6y = 20 Solution _________

9. Example 4: -25x – 30y = -70 Example 5: -7x + 5y = 8 18x + 30y = 42 7x – 5y = 2 Solution _________

10. Example 6: -4x – 2y = -12 Example 7: x – y = 11 4x + 8y = -24 2x + y = 19 Solution _________

11. Match each system of equations with the best method. __________1. 5x + 4y = -1 3x – 4y = 12a. Graphing __________2. x – 2y = 6b. Substitution y = 7x – 3 __________3. y = 8x + 1c. Elimination y = -4x – 2 __________4. 3x + y = 6 -5x + 4y = -10