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Solving Systems by Elimination (multiply)

Algebra 1. 1/4/2020. Solving Systems by Elimination (multiply). Objective : solve a linear system by elimination when first having to make opposites.

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Solving Systems by Elimination (multiply)

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  1. Algebra 1 1/4/2020 Solving Systems by Elimination (multiply) Objective: solve a linear system by elimination when first having to make 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.

  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. Introduction To solve a linear system using __________ first multiply one or both of the equations to make _________. Now add up your two _________ and solve for the remaining variable. Plug that solution back into any equation to find the other ________. elimination opposites equations variable

  4. Warm-Up Solve the system by linear combination.

  5. Notes • Solving a System by Linear Combination 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.

  6. Rules for Special Cases When solving a system of two linear equations in two variables:1. If an identity is obtained, such as 0 = 0, then the system has an infinite number of solutions are dependent and, since a solution exists, the system is consistent. 2. If a contradiction is obtained, such as 0 = 7, then the system has no solution. The system is inconsistent.

  7. 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.

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. Class Work Solve the system by linear combination.

  14. 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.

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

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