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WARNING The work in this PowerPoint is the property of r squared creation. The copying or distribution of this work is ILLEGAL, including but not limited to the posting of the PowerPoint online. Teachers are not exempt in any way, shape, or form. To avoid copyright infringement written permission from the creator is necessary. 2 r creation If you have any questions please contact [email protected]. Copyright 2012 by www.rsquaredcreation.com. All rights reserved. Before We Get Started REMEMBER TO ALWAYS BE RESPECTFUL! NO food or drinks are allowed. • Please put your gum into the trash. NO electronics are allowed. • Please put away cell phones and music players. "Wise men speak because they have something to say; fools because they have to say something.” - Plato Yesterday’s Homework 1. Any questions? 2. Please pass your homework to the front. • Make sure the correct heading is on your paper. • Is your NAME on your paper? • Make sure the homework is 100% complete. • Incomplete work will NOT be accepted. What Do Notes Look Like? • Heading • Date • Section # and Title • IWBAT (I will be able to) • Warm-Up • Notes • You do not have to copy the text in blue! • Class Work • Summary Heading 5/24/2017 6.3A Solving Systems by Elimination (opposites) IWBAT: solve a linear system by elimination when already having opposites. (CA St. 9) Standard 9: Students solve a system of two linear equations in two variables algebraically and are able to interpret the answer graphically. Students are able to solve a system of two linear inequalities in two variables and to sketch the solution sets. Warm-Up Solve the system by substitution. 1. x 3 2 x 4 y 6 2x 4 y 6 2 3 4 y 6 6 4 y 6 6 6 4 y 12 4 4 y 3 3, 3 2. y 2x 3x 4 y 10 3 x 4 y 10 3x 4 2x 10 3x 8x 10 5x 10 5 5 x2 y 2x y 2 2 y4 2, 4 Notes • Solving a System by Elimination 1. Arrange the like variables in columns. - This is already done. 2. Pick a variable, x or y, and make the two equations opposites using multiplication. 3. Add the equations together (eliminating a variable) and solve for the remaining variable. 4. Substitute the answer into one of the ORIGINAL equations and solve. 5. Check your solution. Notes Solve the system by linear combination. Ex. 2x y 5 2 x 3 y 7 4 y 12 4 2x y 5 2x 3 5 3 3 2x 2 2 2 x 1 4 y 3 1, 3 1) Arrange the variables. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer. Notes Solve the system by linear combination. Ex. 2x y 5 2 x 3 y 7 1, 3 Check 2x y 5 2 1 3 5 23 5 55 2 x 3 y 7 2 1 3 3 7 2 9 7 77 1) Arrange the variables. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer. Notes Now you try. Solve the system by linear combination. Ex. 5 x 4 y 6 3x 4 y 2 2 x 4 2 2 x 2 1) Arrange the variables. 2) Make opposites. 5 x 4 y 6 5 2 4 y 6 10 4 y 6 10 10 4y 4 4 4 y 1 2, 1 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer. Notes Solve the system by linear combination. Ex. 5 x 4 y 6 3x 4 y 2 2, 1 Check 5 x 4 y 6 5 2 4 1 6 10 4 6 6 6 3x 4 y 2 3 2 4 1 2 64 2 22 1) Arrange the variables. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer. Notes Now you try. Solve the system by linear combination. Ex. 3x 5 y 2 3x 6 y 6 1y 4 1 1 y 4 1) Arrange the variables. 2) Make opposites. 3x 5 y 2 3x 5 4 2 3x 20 2 20 20 3x 18 3 6, 4 3 x 6 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer. Notes Solve the system by linear combination. Ex. 3x 5 y 2 3x 6 y 6 6, 4 Check 3x 5 y 2 3 6 5 4 2 18 20 2 2 2 3x 6 y 6 3 6 6 4 6 18 24 6 66 1) Arrange the variables. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer. Notes Solve the system by linear combination. Ex. 6 x 7 y 10 6 x 7 y 10 00 Infinite Solutions 1) Arrange the variables. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer. Notes Now you try. Solve the system by linear combination. Ex. 5x 8 y 9 5 x 8 y 2 0 11 No Solution 1) Arrange the variables. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer. Class Work Solve the system by linear combination. 2x 5 y 2 x 4 y 1 1. 2. 3. 2 x 3 y 18 x y 2 6, 2 3, 1 x 2 y 5 5 x 6 y 4 4. 5. 6. 3x 2 y 11 2x 6 y 2 3, 1 2, 1 6 x 2 y 2 3x y 13 7. 8. 9. 6 x 2 y 4 4 x y 16 3, 4 No Solution 10. 3x y 7 x y 1 4, 5 11. 2 x 2 y 18 12. 2 x y 9 6, 3 4 x 3 y 7 4 x 2 y 2 1, 1 3x y 14 2 x y 1 3, 5 5 x 4 y 13 5 x 4 y 13 Infinite Solutions 5 x 2 y 16 x 2 y 8 4, 2 Summary Write a summary about today’s lesson. opposites When a linear system already has ________ just add up both equations and solve for one of the variables. Next plug that solution back into any of the variable equations to find the other ________. original _________ Today’s Homework Worksheet 6.3A Rules for Homework 1. Pencil ONLY. 2. Must show all of your work. • NO WORK = NO CREDIT 3. Must attempt EVERY problem. 4. Always check your answers. Ticket Out the Door Complete the Ticket Out the Door without talking!!!!! Talking = time after the bell! Put your NAME on the paper. When finished, turn your paper face DOWN. Solve the system. 2x 3y 6 2 x 2 y 14 3, 4