Question

If the system of equations $x+2 y+3 z=3$ $4 x+3 y-4 z=4$ $8 x+4 y-\lambda z=9+\mu$ has infinitely many solutions, then the ordered pair $(\lambda, \mu)$ is equal to :

• A. $\left(\frac{72}{5},-\frac{21}{5}\right)$
• B. $\left(\frac{72}{5}, \frac{21}{5}\right)$
• C. $\left(-\frac{72}{5} \cdot-\frac{21}{5}\right)$
• D. $\left(-\frac{72}{5}, \frac{21}{5}\right)$

Answer 1

Answer: (A)

$\left(\frac{72}{5},-\frac{21}{5}\right)$

Answer 2

The correct answer is (A) : $\left(\frac{72}{5},-\frac{21}{5}\right)$
x+2y+3z=3......(i)
4x+3y−4z=4.......(ii)
8x+4y−λz=9+μ......(iii)
(i) ×4 - (ii) ⇒5y+16z=8......(iv)
(ii) ×2− (iii) ⇒2y+(λ−8)z=−1−μ......(v)
(iv) ×2− (iii) ×5⇒(32−5(λ−8))z=16−5(−1−μ)
For infinite solutions ⇒72−5λ=0⇒λ=572​
21+5μ=0⇒μ=5−21​
⇒(λ,μ)≡(572​,5−21​)