Khan Academy
- $\rhd$ Intro to Systems with Three Variables (8:23) Solve the system algebraically and graphically: $$\begin{cases}x + y – 3z = -10\\ x – y + 2z = 3\\ 2x + y – z = -6\end{cases}$$
- $\rhd$ Solving Linear Systems with Three Variables (7:00) Uses the method of variable elimination to solve:
$$\begin{cases} x + 2y – 5z = -17\\2x – 3y + 2z = -16\\3x + y – z = 3\end{cases}$$
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Solving Linear Systems with 3 Variables: no solution (5:05)
Determine whether this system has infinitely many or no solutions.
$$\begin{cases}2x – 4y + z = 3\\8x – 2y + 4z = 7\\-4x + y – 2z = -14\end{cases}$$
- 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: $$\begin{cases}2x-y+z=3\\5x+2y-3z=1\\2x+y-z = 2\end{cases}$$
2. 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. Solving a 3-D system of equations using elimination by addition (8:18) Solve the system:
$$\begin{cases}4x-4y+8z=20\\8x+4y-4z=4\\12x-8y-12z=-40\end{cases}$$
