Question

Find the solution of the pair of equations x/10+ y/5 - 1 = 0 and x/8 + y/6 = 15 . Hence , find λ , if y = λx + 5.

Answer 1

Answer:

The value of $\lambda=-\frac{1}{2}$

Step-by-step explanation:

Given : The pair of equations $\frac{x}{10}+\frac{y}{5}-1=0$ and  $\frac{x}{8}+\frac{y}{6}=15$

To find : The value of $\lambda$, if $y = \lambda  x + 5$

Solution :

Let $\frac{x}{10}+\frac{y}{5}-1=0$ ........(1)

$\frac{x}{8}+\frac{y}{6}=15$  .........(2)

Solving equation (1), by taking LCM

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

$x+2y=10$ ......(3)

Solving equation (2), by taking LCM

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

$6x+8y=720$

$3x+4y=360$ ......(4)

Multiply equation (3) by 3 and subtract from (4),

$3x+4y-3x-6y=360-30$

$-2y=330$

$y=-165$

Substitute the value of y in equation (3),

$x+2y=10$

$x+2(-165)=10$

$x-330=10$

$x=340$

Now, Substitute the value of x and y in the expression $y = \lambda x+5$

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

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

$-170= \lambda(340)$

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

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

Therefore, The value of $\lambda=-\frac{1}{2}$

Answer 2

hope it helps

mark as brainliest