Solving Systems of Equation Using Elimination

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

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.

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

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 _________

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)

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

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

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

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