Find the solution of the pair of equations $ \frac{x}{10}+\frac{y}{5}-1=0 $ and $ \frac{x}{8}+\frac{y}{6}=15 $. Hence, find $ \lambda $, if $ y=\lambda x+5 $.

AcademicMathematicsNCERTClass 10


The given pair of equations is $\frac{x}{10}+\frac{y}{5}-1=0$ and $\frac{x}{8}+\frac{y}{6}=15$ and $y = \lambda x + 5$.

To do:

We have to solve the given system of equations and the value of $\lambda$. 


The given system of equations can be written as,


$\Rightarrow \frac{1(x)+2(y)}{10}=1$

$\Rightarrow x+2y=1(10)$   (On cross  multiplication)

$\Rightarrow x+2y=10$---(i)


$\Rightarrow \frac{3(x)+4(y)}{24}=15$   (LCM of 8 and 6 is 24)

$\Rightarrow 3x+4y=15(24)$   (On cross multiplication)

$\Rightarrow 3x=360-4y$

$\Rightarrow x=\frac{360-4y}{3}$----(ii)

Substitute $x=\frac{360-4y}{3}$ in equation (i), we get,


Multiplying by $3$ on both sides, we get,







Substituting the value of $y=-165$ in equation (ii), we get,





$y = \lambda x + 5$   (Given)

$-165=\lambda (340)+5$




Therefore, the solution of the given system of equations is $x=340$, $y=-165$ and the value of $\lambda$ is $\frac{-1}{2}$.  

Updated on 10-Oct-2022 13:27:15