Solving 3 variable systems of equations by elimination

Solving 3 variable systems of equations by elimination

Lessons

The idea of elimination is to convert 3 equations with 3 variables to 2 equations with 2 variables, then to 1 equation with 1 variable.

  • 1.
    Solving Three Variable Systems of Equations by Substitution – (Easy)

    Solve the following system of equations by elimination:

    x4y+z=12x - 4y + z = -12

    x+3yz=6x + 3y - z = 6

    2x2y+z=52x - 2y + z = 5


  • 2.
    Solving Three Variable Systems of Equations by Substitution – (Medium)

    Solve the following system of equations by elimination:

    4x3y+2z=204x - 3y + 2z = 20

    2x4y+3z=3-2x - 4y + 3z = 3

    x+yz=2x + y - z = 2


  • 3.
    Solving Three Variable Systems of Equations by Substitution – (Hard)

    Solve the following system of equations by elimination:

    x+4y+7z=109x + 4y + 7z = 109

    4x5y+4z=294x - 5y + 4z = -29

    5x+yz=105x + y - z = 10