Home/Class 10/Maths/

Find the value of x and y in the following equations:
$$\dfrac{10}{x+y}+\dfrac{2}{x-y}=4$$
$$\dfrac{15}{x+y}-\dfrac{5}{x-y}=-2$$
Speed
00:00
03:58

## QuestionMathsClass 10

Find the value of x and y in the following equations:
$$\dfrac{10}{x+y}+\dfrac{2}{x-y}=4$$
$$\dfrac{15}{x+y}-\dfrac{5}{x-y}=-2$$

$$x=3, y=2$$
4.6
4.6

## Solution

Given:
$$\dfrac{10}{x+y}+\dfrac{2}{x-y}=4$$
$$\dfrac{15}{x+y}-\dfrac{5}{x-y}=-2$$
Substituting $$\frac{1}{x+y} = m$$ and $$\frac{1}{x-y} = n$$ in the given equations, we get,
$$10m + 2n = 4 \implies 10m + 2n – 4 = 0$$....  (i)
$$15m – 5n = -2 \implies 15m – 5n + 2 = 0$$...  (ii)
Using cross-multiplication method, we get,
$$\dfrac{m}{4-20}=\dfrac{n}{-60-(20)}=\dfrac{1}{-50-30}$$
$$\dfrac{m}{-16}=\dfrac{n}{-80}=\dfrac{1}{-80}$$
$$\dfrac{m}{-16}=\dfrac{1}{-80}$$and$$\dfrac{n}{-80}=\dfrac{1}{-80}$$
$$m=\dfrac{1}{5}$$and $$n=1$$
$$m=\dfrac{1}{x+y}=\dfrac{1}{5}$$ and $$n=\dfrac{1}{x-y}=1$$
$$x + y = 5$$ .... (iii)
and $$x – y = 1$$ .....  (iv)
Adding equation (iii) and (iv), we get
$$2x = 6 \implies x = 3$$ .....  (v)
Putting the value of $$x = 3$$ in equation (3), we get
$$y = 2$$
Hence, $$x = 3$$ and $$y = 2$$