Matrices & Determinants
Infinitely Many Solutions — Finding α+β
nta_pyq_2023_apr
Grade 12
Question:
If the system $7x+11y+\alpha z=13$, $5x+4y+7z=\beta$, $175x+194y+57z=361$ has infinitely many solutions, then $\alpha+\beta+2$ is equal to
Step-by-Step Solution
Key Concept: For infinite solutions: $\Delta=0$ gives $\alpha=-9$ and $\Delta_1=0$ gives $\beta=11$.
$\alpha=-9,\ \beta=11$. $\alpha+\beta+2=4$.
Correct Answer: 1