x+2y+3z+4t+5p=a
2x-y+3z+5t-4p=b
3x+3y+4z+2t-p=c
4x-y-z+t+2p=d
x+y+5z-t+p=e
You asked:
Solve the system of equations:\[\begin{aligned}x + 2 y + 3 z + 4 t + 5 p &= a\\2 x - y + 3 z + 5 t - 4 p &= b\\3 x + 3 y + 4 z + 2 t - p &= c\\4 x - y - z + t + 2 p &= d\\x + y + 5 z - t + p &= e\end{aligned}\]
MathBot Answer:
The system of equations has infinitely many solutions.
$$\begin{aligned}a &= 9 t - 4 x - 3 y - 22 z + 5 e\\b &= t + 6 x + 3 y + 23 z - 4 e\\c &= t + 4 x + 4 y + 9 z - e\\d &= 3 t + 2 x - 3 y - 11 z + 2 e\\p &= t - x - y - 5 z + e\end{aligned}$$\(t\) is a free variable.
\(x\) is a free variable.
\(y\) is a free variable.
\(z\) is a free variable.