Question

2/x+5/y=1 and 60/x-20/y=13 for these equations these vaule of xand y will b

Answer 1

Hope it helps you...

Answer 2

The value of x and y is 4 and 10 in equations $\frac{2}{x} + \frac{5}{y} = 1$and $\frac{60}{x} - \frac{20}{y} = 13$

Concept used:

If the given equations involve 1/x and 1/y, then put 1/x = p and 1/y = q , to convert them into linear form. After solving, put the values of p and q in above substitutions, to get the value of x and y.

Given :

$\frac{2}{x} + \frac{5}{y} = 1$      ….......(1)

$\frac{60}{x} - \frac{20}{y} = 13$   ….....(2)

To find:

The value of x and y

Solution:

Step1: Convert the given equation into linear form by making some suitable substitution:

Given, pair of equations is not linear.

Let $\frac{1}{x} = p$  and $\frac{1}{y} = q$ we get,

2p + 5q = 1……….(3)

60p -  20q = 13………(4)

These above equations 3 and 4 are a pair of linear equations.

Step 2: Multiply eq 3 by 4:  

8p + 20q = 4 …….(5)

Step 3 : Solve eq. 4 and 5 by elimination method:

By adding both the equations, we get,

60p -  20q = 13

8p + 20q = 4

---------------------------

68 p = 17

p = $\frac{17}{68}$

p = $\frac{1}{4}$

Step 4: Putting the value of p = $\frac{1}{4}$ in eq 5:

8p + 20q = 4

8($\frac{1}{4}$) + 20q = 4

2 + 20q = 4

20q = 4 - 2

20q = 2

q = $\frac{2}{20}$

q = $\frac{1}{10}$

Step 5: Put these values of p and q in above substitutions to find the value of x and y:

Since, $\frac{1}{x} = p$  and $\frac{1}{y} = q$

On putting the values of p and q we get,

$\frac{1}{x} = \frac{1}{4}$  and $\frac{1}{y} = \frac{1}{10}$

x = 4 and y = 10

Hence, x = 4 and y = 10 is the required solution.

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