Question

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

• A. $\frac{-165}{17}$
• B. $\frac{-1}{2}$
• C. $\frac{361}{696}$
• D. $\frac{340}{17}$

Answer 1

The correct option is B $\frac{-1}{2}$

$\frac{x}{10}+\frac{y}{5}-1=0$

$\frac{x}{10}+\frac{y}{5}=1$

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

$x+2y=10$.....................(1)

now consider,$\frac{x}{8}+\frac{y}{6}=15$

$\frac{6x+8y}{48}=15$

$3x+4y=24\times 15=360$.................................(2)

now multiply (1)by 3

$3x+6y=30$ ........................(3)

subtracting (2) and (3)

$2y=-330$

$y=-165$

put in(1)

$x+2(-165)=10$

$x-330=10$

$x=340$

now, $y=\lambda x+5$

$⟹-165=\lambda \left(340\right)+5$

$-170=\lambda \left(340\right)$

$\lambda =\frac{-170}{340}=\frac{-1}{2}$