2x+y+3z-w=0
7x+4y+3z-3w=0
5x+7y+7z+8w=0
You asked:
Solve the system of equations:\[\begin{aligned}2 x + y + 3 z - w &= 0\\7 x + 4 y + 3 z - 3 w &= 0\\5 x + 7 y + 7 z + 8 w &= 0\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}w &= - \frac{67 z}{6}\\x &= - \frac{121 z}{6}\\y &= \frac{157 z}{6}\end{aligned}$$
\(z\) is a free variable.