Name _____________________________________________ Date ______________ Period ________ Notes: Section 5.2 Day 3: Solving Systems of Linear Equations by Elimination (including Section 5.5: Inconsistent and Dependent Systems of Linear Equations) Learning Targets I can solve systems of linear equations using the elimination method. 8.EE.8b WARM-­‐UP We have already learned to solve systems of equations by using the substitution method… a.
2h + 3k = 13 h = 2k – 4 b.
3m + b = 23 m – b = 5 ***Today we will learn to solve systems algebraically using Elimination.*** The Elimination Method 1. Look for (or make) exact opposites. 2. Add down. J 3. Simplify and solve. 4. Find the value of the other variable. 5. Write your solution as a coordinate point (x, y). Examples: Solve the following systems using the Elimination Method. Guided Practice #2 in the text: Example #2 in the text: 2x – y = 2 4x + y = 9 3x + y = 13 3x – y = 5 G8 5.2 Day 3 Student Notes: Elimination Method p. 1 x + y = 8 x + 2y = 10 Guided Practice #3 in the text: Guided Practice #1 in the text: 2x + 3y = 7 x + 6y = 8 x + 6y = 1 x + y = 6 2a + 3b = 29 2a – b = 17 Example #3 in the text: Guided Practice #4 in the text: 2x + 5y = 11 9x + 2y = -­‐12 7m + 2n = -­‐8 2m = 3n – 13 Guided Practice #5 in the text: Guided Practice #6 in the text: 3x – 2y = 24 5x + 4y = -­‐4 2x + 7y = -­‐32 4x – 5y = 12 G8 5.2 Day 3 Student Notes: Elimination Method p. 2 Identify whether the following systems of equations are inconsistent (no solutions), dependent (infinitely many solutions), or consistent (one unique solution). Justify your answer. Solve the system of equations if it has one unique solution. 2x + y = 1 4x + 2y = 4 12x + 4y = 16 9x + 3y = 12 10x + 5y = 15 2x + y = 3 3x + y = 4 6x + 2y = 14 2x + y = 8 4x – 2y = 24 -­‐15x + 3y = 3 -­‐5x + y = 21 Remember: If something weird happens but you end up with a TRUE statement (for example: x = x, 2 = 2, or 0 = 0) the system has infinitely many solutions (it is a dependent system). If something weird happens but you end up with a FALSE statement (for example: 0 = 2) the system has no solutions (it is an inconsistent system). PRACTICE: 5.2 Day 3 Elimination Method Homework G8 5.2 Day 3 Student Notes: Elimination Method p. 3