Systems of Linear Equations in Three Variables

Khan Academy

1. $⊳$ Intro to Systems with Three Variables (8:23) Solve the system algebraically and graphically:    $$\{\begin{array}{l}x+y–3z=-10\\ x–y+2z=3\\ 2x+y–z=-6\end{array}$$
2.  $⊳$ Solving Linear Systems with Three Variables (7:00) Uses the method of variable elimination to solve:
   $$\{\begin{array}{l}x+2y–5z=-17\\ 2x–3y+2z=-16\\ 3x+y–z=3\end{array}$$
3.   Solving Linear Systems with 3 Variables: no solution (5:05)
   Determine whether this system has infinitely many or no solutions.
   $$\{\begin{array}{l}2x–4y+z=3\\ 8x–2y+4z=7\\ -4x+y–2z=-14\end{array}$$
4.   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. Solving a 3-D system of equations using elimination by addition (6:46) Solve the system: $$\{\begin{array}{l}2x-y+z=3\\ 5x+2y-3z=1\\ 2x+y-z=2\end{array}$$

2. Solving a 3-D system of equations using elimination by addition (4:15) Solve the system: $$\{\begin{array}{l}x+2y+z=12\\ 2x-2y-z=-6\\ x+2y-z=2\end{array}$$

3. Solving a 3-D system of equations using elimination by addition (8:18) Solve the system:
$$\{\begin{array}{l}4x-4y+8z=20\\ 8x+4y-4z=4\\ 12x-8y-12z=-40\end{array}$$