SolveSysByElimAddSub

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SolveSysByElimAddSub

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  1. Objective

    Slide 1 - Objective

    • The student will be able to:
    • solve systems of equations using elimination with addition and subtraction.
    • SOL: A.4e
    • Designed by Skip Tyler, Varina High School
  2. Solving Systems of Equations

    Slide 2 - Solving Systems of Equations

    • So far, we have solved systems using graphing and substitution. These notes show how to solve the system algebraically using ELIMINATION with addition and subtraction.
    • Elimination is easiest when the equations are in standard form.
  3. Slide 3

    • Solving a system of equations by elimination using addition and subtraction.
    • Step 1: Put the equations in Standard Form.
    • Step 2: Determine which variable to eliminate.
    • Step 3: Add the equations.
    • Step 4: Plug back in to find the other variable.
    • Step 5: Check your solution.
    • Standard Form: Ax + By = C
    • Look for variables that have the
    • same coefficient.
    • Solve for the variable.
    • Substitute the value of the variable
    • into the equation.
    • Substitute your ordered pair into
    • BOTH equations.
  4. 1) Solve the system using elimination.

    Slide 4 - 1) Solve the system using elimination.

    • x + y = 5
    • 3x – y = 7
    • Step 1: Put the equations in Standard Form.
    • Step 2: Determine which variable to eliminate.
    • They already are!
    • The y’s have the same
    • coefficient.
    • Step 3: Add or subtract the equations.
    • Add to eliminate y.
    • x + y = 5
    • (+) 3x – y = 7
    • 4x = 12
    • x = 3
  5. 1) Solve the system using elimination.

    Slide 5 - 1) Solve the system using elimination.

    • Step 4: Plug back in to find the other variable.
    • x + y = 5
    • (3) + y = 5
    • y = 2
    • Step 5: Check your solution.
    • (3, 2)
    • (3) + (2) = 5
    • 3(3) - (2) = 7
    • The solution is (3, 2). What do you think the answer would be if you solved using substitution?
    • x + y = 5
    • 3x – y = 7
  6. Solve using elimination.

    Slide 6 - Solve using elimination.

    • 2x – 3y = -2
    • x + 3y = 17
    • (2, 2)
    • (9, 3)
    • (4, 5)
    • (5, 4)
  7. 3) Solve the system using elimination.

    Slide 7 - 3) Solve the system using elimination.

    • y = 7 – 2x
    • 4x - y = 5
    • Step 1: Put the equations in Standard Form.
    • 2x + y = 7
    • 4x + y = 5
    • Step 2: Determine which variable to eliminate.
    • The y’s have the same
    • coefficient.
    • Step 3: Add or subtract the equations.
  8. 2) Solve the system using elimination.

    Slide 8 - 2) Solve the system using elimination.

    • Step 4: Plug back in to find the other variable.
    • y = 7 – 2x
    • y = 7 – 2(2)
    • y = 3
    • Step 5: Check your solution.
    • (2, 3)
    • (3) = 7 – 2(2)
    • 4(2) - (3) = 5
    • y = 7 – 2x
    • 4x - y = 5
  9. Find two numbers whose sum is 18 and whose difference 22.

    Slide 10 - Find two numbers whose sum is 18 and whose difference 22.

  10. Find two numbers whose sum is 18 and whose difference 22.

    Slide 11 - Find two numbers whose sum is 18 and whose difference 22.

    • 14 and 4
    • 20 and -2
    • 24 and -6
    • 30 and 8