For a unique value of ‘μ’ and ‘λ ‘ the system of equations given byx+y+z=6x+2y+3z=142x+5y+λz=μhas infinitely many solutions, then μ−λ4=_____

# For a unique value of '$\mathrm{\mu }$' and '$\mathrm{\lambda }$ ' the system of equations given by$\begin{array}{l}\mathrm{x}+\mathrm{y}+\mathrm{z}=6\\ \mathrm{x}+2\mathrm{y}+3\mathrm{z}=14\\ 2\mathrm{x}+5\mathrm{y}+\mathrm{\lambda z}=\mathrm{\mu }\end{array}$has infinitely many solutions, then $\frac{\mathrm{\mu }-\mathrm{\lambda }}{4}=\mathrm{_____}$

Fill Out the Form for Expert Academic Guidance!l

+91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)

### Solution:

$\begin{array}{l}\mathrm{y}+2\mathrm{z}=8\\ \mathrm{y}+\left(\mathrm{\lambda }-6\right)\mathrm{z}=\mathrm{\mu }-28\\ 1=\frac{2}{\mathrm{\lambda }-6}=\frac{8}{\mathrm{\mu }-28}\\ \mathrm{\lambda }=8;\mathrm{\mu }=36\\ \frac{\mathrm{\mu }-\mathrm{\lambda }}{4}=\frac{28}{4}=7\end{array}$  +91

Live ClassesBooksTest SeriesSelf Learning

Verify OTP Code (required)