3-D Systems of Equations

Khan Academy

  1. \rhd Intro to Systems with Three Variables (8:23) Solve the system algebraically and graphically:   

        \[\begin{cases}x +  y  -  3z  =  -10\\ x  -  y  +  2z  =  3\\ 2x  +  y  -  z  =  -6\end{cases}\]

  2.  \rhd Solving Linear Systems with Three Variables (7:00) Uses the method of variable elimination to solve:

        \[\begin{cases} x  +  2y  -  5z  =  -17\\2x  -  3y  +  2z  =  -16\\3x  +  y  -  z  =  3\end{cases}\]

  3.  \rhd Solving Linear Systems with 3 Variables: no solution (5:05)
    Determine whether this system has infinitely many or no solutions.

        \[\begin{cases}2x  -  4y  +  z  =  3\\8x  -  2y  +  4z  =  7\\-4x  +  y  -  2z  = -14\end{cases}\]

  4.  \rhd Three variable linear system word problem (8:15)  The second angle of a triangle is 50 degrees less than 4 times the first angle. The third angle is 40 degrees less than the first angle.  Find the measures of the three angles.

PatrickJMT:

1. \rhd Solving a 3-D system of equations using elimination by addition (6:46) Solve the system:

    \[\begin{cases}2x-y+z=3\\5x+2y-3z=1\\2x+y-z = 2\end{cases}\]

2. \rhd Solving a 3-D system of equations using elimination by addition (4:15) Solve the system:

    \[\begin{cases}x+2y + z =12\\2x-2y-z=-6\\x+2y-z= 2\end{cases}\]

3. \rhd Solving a 3-D system of equations using elimination by addition (8:18) Solve the system:

    \[\begin{cases}4x-4y+8z=20\\8x+4y-4z=4\\12x-8y-12z=-40\end{cases}\]