Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.

Solving systems with elimination

596 views

Published on

Published in: Technology
  • Be the first to comment

  • Be the first to like this

Solving systems with elimination

  1. 1. ObjectiveThe student will be able to:solve systems of equations usingelimination with addition and subtraction.
  2. 2. Solving Systems of EquationsSo far, we have solved systems usinggraphing and substitution. These notesshow how to solve the systemalgebraically using ELIMINATION withaddition and subtraction.Elimination is easiest when theequations are in standard form.
  3. 3. Solving a system of equations by eliminationusing addition and subtraction.Step 1: Put the equations inStandard Form.Step 2: Determine whichvariable to eliminate.Step 3: Add or subtract theequations.Step 4: Plug back in to findthe other variable.Step 5: Check yoursolution.Standard Form: Ax + By = CLook for variables that have thesame coefficient.Solve for the variable.Substitute the value of the variableinto the equation.Substitute your ordered pair intoBOTH equations.
  4. 4. 1) Solve the system using elimination.x + y = 53x – y = 7Step 1: Put the equations inStandard Form.Step 2: Determine whichvariable to eliminate.They already are!The y’s have the samecoefficient.Step 3: Add or subtract theequations.Add to eliminate y.x + y = 5(+) 3x – y = 74x = 12x = 3
  5. 5. 1) Solve the system using elimination.Step 4: Plug back in to findthe other variable.x + y = 5(3) + y = 5y = 2Step 5: Check yoursolution.(3, 2)(3) + (2) = 53(3) - (2) = 7The solution is (3, 2). What do you think the answerwould be if you solved using substitution?x + y = 53x – y = 7
  6. 6. 2) Solve the system using elimination.4x + y = 74x – 2y = -2Step 1: Put the equations inStandard Form.They already are!Step 2: Determine whichvariable to eliminate.The x’s have the samecoefficient.Step 3: Add or subtract theequations.Subtract to eliminate x.4x + y = 7(-) 4x – 2y = -23y = 9y = 3Remember to“keep-change-change”
  7. 7. 2) Solve the system using elimination.Step 4: Plug back in to findthe other variable.4x + y = 74x + (3) = 74x = 4x = 1Step 5: Check yoursolution.(1, 3)4(1) + (3) = 74(1) - 2(3) = -24x + y = 74x – 2y = -2
  8. 8. Which step would eliminate a variable?3x + y = 43x + 4y = 61. Isolate y in the firstequation2. Add the equations3. Subtract the equations4. Multiply the firstequation by -4
  9. 9. Solve using elimination.2x – 3y = -2x + 3y = 171. (2, 2)2. (9, 3)3. (4, 5)4. (5, 4)
  10. 10. 3) Solve the system using elimination.y = 7 – 2x4x + y = 5Step 1: Put the equations inStandard Form.2x + y = 74x + y = 5Step 2: Determine whichvariable to eliminate.The y’s have the samecoefficient.Step 3: Add or subtract theequations.Subtract to eliminate y.2x + y = 7(-) 4x + y = 5-2x = 2x = -1
  11. 11. 2) Solve the system using elimination.Step 4: Plug back in to findthe other variable.y = 7 – 2xy = 7 – 2(-1)y = 9Step 5: Check yoursolution.(-1, 9)(9) = 7 – 2(-1)4(-1) + (9) = 5y = 7 – 2x4x + y = 5
  12. 12. What is the first step when solving withelimination?1. Add or subtract the equations.2. Plug numbers into theequation.3. Solve for a variable.4. Check your answer.5. Determine which variable toeliminate.6. Put the equations in standardform.
  13. 13. Find two numbers whose sum is 18and whose difference 22.1. 14 and 42. 20 and -23. 24 and -64. 30 and 8

×