Question

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

Answer 1

Given pair of equation is
$\frac{x}{10}+\frac{y}{5}-1=0$
Now, multiplying both sides of Eq. (i) by LCM (10, 5) = 10, we get
x + 2y – 10 = 0
$\Rightarrow$ x + 2y = 10
Again, multiplying both sides of Eq. (iv) by LCM (8, 6) = 24, we get
3x + 4y = 360
On, multiplying Eq. (iii) by 2 and then subtracting from Eq. (iv), we get
(3x + 4y = 360) - $(2x+4y=20)Hence,x=340$
put the value of x in Eq. (iii), we get
340 + 2y = 10
$\Rightarrow$ 2y = 10 – 340 = - 330
$\Rightarrow$ y = -165
Given that, the linear relation between x, y and $\lambda$ is
Now, put the values of x and y in above relation, we get
$-165=\lambda \left(340\right)+5\Rightarrow 340\lambda =-170\Rightarrow \lambda =-\frac{1}{2}$
Hence, the solution of the pair of equations is x = 340, y = - 165 and the required value is - $\frac{1}{2}$