𝑥 + 2𝑦 + 𝑧 + 3𝑤 = 1
𝑥 + 𝑦 − 𝑧 + 2𝑤 = 0
𝑥 + 2𝑦 − 𝑧 + 𝑤 = 1
𝑥 + 3𝑦 + 3𝑧 + 4𝑤 = 2
You asked:
Solve the system of equations:\[\begin{aligned}x + 2 y + z + 3 w &= 1\\x + y - z + 2 w &= 0\\x + 2 y - z + w &= 1\\x + 3 y + 3 z + 4 w &= 2\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}w &= - z\\x &= 4 z - 1\\y &= 1 - z\end{aligned}$$
\(z\) is a free variable.