Matrices & Determinants
Infinite Solutions Then Second System
nta_pyq_2023_jan
Grade 12
Question:
Let the system $x+y+kz=2$, $2x+3y-z=1$, $3x+4y+2z=k$ have infinitely many solutions. Then the system $(k+1)x+(2k-1)y=7$, $(2k+1)x+(k+5)y=10$ has:
infinitely many solutions
unique solution satisfying $x-y=1$
no solution
unique solution satisfying $x+y=1$
Step-by-Step Solution
Key Concept: $\Delta=0$: $\begin{vmatrix}1&1&k\\2&3&-1\\3&4&2\end{vmatrix}=10-7-k=3-k=0\Rightarrow k=3$.
Unique solution satisfying $x+y=1$.
Correct Answer: 4