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# Solving systems with elimination

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### 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