Matrices & Determinants
Infinite Solutions — Finding Expression
nta_pyq_2024_apr
Grade 12
Question:
If the system of equations $x+4y-z=\lambda$, $7x+9y+\mu z=-3$, $5x+y+2z=-1$ has infinitely many solutions, then $(2\mu+3\lambda)$ is equal to:
Step-by-Step Solution
Key Concept: Set $\Delta=0$: gives $\mu=0$. Set $\Delta_x=0$: gives $\lambda=-1$.
$\mu=0$, $\lambda=-1$. $2(0)+3(-1)=-3$.
Correct Answer: 2