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Transcript
Algebra I –Wilsen Unit 6: Systems of Equations Day Five BLOCK 2 Solving Systems of Equations: Elimination We have already learned to solve systems of equations using substitution. Now we will learn to solve them using ELIMINATION. To solve a system of equations using elimination, follow these steps: Step 1: Add the equations together so that either the x’s or the y’s are eliminated (that is, they cancel out). Step 2: Solve the resulting equation for x or y, whichever still exists. Step 3: Substitute to find the value of the other variable. ________________________________________________________________________ Example 1: x + y = 19 x–y =9 The final solution is x = ____, y = ____ Example 2: 3x + 2y = 7 –3x + y = –1 The final solution is x = ____, y = ____ Step 1: If the x’s or y’s won’t cross out, multiply an entire equation by a number to get either x's or y's to match. Step 2: Add the equations together so that either the x’s or the y’s are eliminated (that is, they cancel out). Step 4: Solve the resulting equation for x or y, whichever still exists. Step 5: Substitute to find the value of the other variable. ________________________________________________________________________ Example 3: –2x + 5y = 11 x + 2y = 8 The final solution is x = ____, y = ____ ________________________________________________________________________ Example 4: 2x + y = –2 –3x + 4y = 14 The final solution is x = ____, y = ____ Solve each of the following systems of equations using the elimination method. Remember, you can check your answers!! 1. 2x + y = 3 3x – y = –8 x = __________ y = __________ 2. x + 3y = –3 –x + y = –5 x = __________ y = __________ 3. x + 2y = 17 3x – 2y = 11 x = __________ y = __________ 4. 2x + 2y = 18 3x – 2y = –8 x = __________ y = __________ 5. x + 5y = –14 –x + 2y = –7 x = __________ y = __________ 6. x + 2y = –4 6x – 2y = –38 x = __________ y = __________