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Solving Linear Systems: Substitution vs. Elimination

Learn strategies to solve linear systems by substitution and elimination methods algebraically and graphically. Practice solving equations and inequalities in two variables with step-by-step guidance.

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Solving Linear Systems: Substitution vs. Elimination

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  1. Bell Work 2/11/2015 Solve the system by substitution.

  2. Yesterday’s Homework • Any questions? • 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.

  3. Heading 1/4/2020 Solving Systems by Elimination (opposites) TSWBAT: solve a linear system by elimination when already having opposites. 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.

  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.

  5. Notes Solve the system by linear combination. 1) Arrange the variables. Ex. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer.

  6. Notes Solve the system by linear combination. 1) Arrange the variables. Ex. 2) Make opposites. Check 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer.

  7. Notes Now you try. 1) Arrange the variables. Solve the system by linear combination. Ex. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer.

  8. Notes Solve the system by linear combination. 1) Arrange the variables. Ex. 2) Make opposites. Check 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer.

  9. Notes Now you try. Solve the system by linear combination. 1) Arrange the variables. Ex. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer.

  10. Notes Solve the system by linear combination. 1) Arrange the variables. Ex. 2) Make opposites. Check 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer.

  11. Notes Solve the system by linear combination. 1) Arrange the variables. Ex. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer.

  12. Notes Now you try. 1) Arrange the variables. Solve the system by linear combination. Ex. 2) Make opposites. 3) Add and solve for the variable. 4) Substitute into ANY original equation. 5) Check your answer.

  13. Summary • 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 original _________ to find the other ________. • variable • equations

  14. Today’s Homework • Rules for Homework • Pencil ONLY. • Must show all of your work. • NO WORK = NO CREDIT • Must attempt EVERY problem. • Always check your answers.

  15. Homework 6.3A Solve the system by linear combination.

  16. 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.

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