The number of solutions of the system of the system of equations $x+2 y+z=3,2 x+3 y+z=3,3 x+5 y+2 z=1$ is___________
The given system of equations is $x+2 y+z=3,2 x+3 y+z=3$ and $3 x+5 y+2 z=1$.
$\Delta=\left|\begin{array}{lll}1 & 2 & 1 \\ 2 & 3 & 1 \\ 3 & 5 & 2\end{array}\right|=1(6-5)-2(4-3)+1(4-3)=1-2+1=0$
$\Delta_{x}=\left|\begin{array}{lll}3 & 2 & 1 \\ 3 & 3 & 1 \\ 1 & 5 & 2\end{array}\right|=3(6-5)-2(6-1)+1(15-3)=3-10+12=5 \neq 0$
Here, $\Delta=0$ and at least one of $\Delta_{x}, \Delta_{y}$ and $\Delta_{z}$ is not zero, so the given system of equations has no solution.
Thus, the given system of equations has no solution.
The number of solutions of the system of the system of equations x + 2y + z = 3, 2x + 3y + z = 3, 3x + 5y + 2z = 1 is ___0___
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.