If the system of equations $x+2y-3z=2$, $2x+\lambda y+5z=5$, $14x+3y+\mu z=33$ has infinitely many solutions, then $\lambda+\mu$ is equal to :

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] For infinitely many solutions $E_3=aE_1+bE_2$. $x$-coefficient: $a+2b=14$; constant: $2a+5b=33$, so $b=5$, $a=4$. $z$: $\mu=-3a+5b=13$. $y$: $3=2a+\lambda b=8+5\lambda\Rightarrow\lambda=-1$. $\lambda+\mu=12$. Answer (3).

Q. If the system of equations $x+2y-3z=2$, $2x+\lambda y+5z=5$, $14x+3y+\mu z=33$ has infinitely many solutions, then $\lambda+\mu$ is equal to :

Explanation

Reviewed by Dr. Abubacker

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