###### Advertisements

###### Advertisements

Find the solution of the pair of the equation :`3/x + 8/y = - 1; 1/x - 2/y = 2`, x, y ≠ 0

###### Advertisements

#### Solution

The given equations are

`3/x + 8/y = - 1` ...(1)

`1/x - 2/y = 2` ...(2)

Let `1/x = u and 1/y = v`

(1) and (2) will become

3u + 8v = -1 ...(3)

u - 2v = 2 ...(4)

Multiply (4) with 4

4u - 8v = 8 ...(5)

Adding (3) and (5) we get

7u = 7

⇒ u = 1

Putting this value in (4)

1 - 2v = 2

⇒ v = `(-1)/2`

Now

`1/x = u`

⇒ `1/x = 1`

⇒ x = 1

And

`1/y = v`

⇒ `1/y = (-1)/2`

⇒ y = - 2

#### RELATED QUESTIONS

If the point (3, 2) lies on the graph of the equation 5x + ay = 19, then find a.

Solve the following pair of linear equations by the substitution method.

0.2x + 0.3y = 1.3

0.4x + 0.5y = 2.3

Solve the following pair of linear equations by the substitution method

`sqrt2x + sqrt3y = 0`

`sqrt3x - sqrt8y = 0`

**Form the pair of linear equations for the following problems and find their solution by substitution method.**

The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Solve the following systems of equations:

7(y + 3) − 2(x + 2) = 14

4(y − 2) + 3(x − 3) = 2

Solve the following systems of equations:

`(x + y)/(xy) = 2`

`(x - y)/(xy) = 6`

5 pens and 6 pencils together cost Rs 9 and 3 pens and 2 pencils cost Rs 5. Find the cost of

1 pen and 1 pencil.

Solve the following simultaneous equations by Cramer's method.

`x+y=7,2x-3y=9`

**Solve the following set of simultaneous equation.**

x + y = 4 ; 2x - 5y = 1

**Solve the following set of simultaneous equation. **

2x + y = 5; 3x - y = 5

**Solve the following set of simultaneous equation.**

3x - 5y = 16; x - 3y = 8

**Solve the following set of simultaneous equation.**

2y - x = 0; 10x + 15y = 105

**Solve the following set of simultaneous equation.**

2x + 3y + 4 = 0; x - 5y = 11

**Solve the following set of simultaneous equation.**

2x - 7y = 7; 3x + y = 22

The sum of ages of Priyanka and Deepika is 34 years. Priyanka is elder to Deepika by 6 years. Then find their today's ages.

The price of 3 chairs and 2 tables is 4500 rupees and price of 5 chairs and 3 tables is 7000 rupees, then find the price of 2 chairs and 2 tables.

Divide a rope of length 560 cm into 2 parts such that twice the length of the smaller part is equal to `1/3` of the larger part. Then find the length of the larger part.

If 49x – 57y = 172 and 57x – 49y = 252 then x + y = ?

The solution of the equation 2x – y = 2 is ______

The solution of the equation x − y = 10 and x + y = 70 is ______

For the equation 4x + 5y = 20 find y when x = 0

If x + 2y = 5 and 2x + y = 7, then find the value of x + y

Complete the table to draw the graph of 2x – 3y = 3,

x | − 6 | `square` |

y | `square` | 1 |

(x, y) | `square` | `square` |

In the equation 2x – y = 2 if x = 3, then find y = ?

For the equation a + 2b = 7, find a when b = 4

Using variables a and b write any two equations whose solution is (0, 2).

A person starts a job with a fixed salary and yearly increment. After 4 years his salary is ₹ 15000 and after 10 years it becomes ₹ 18000. Then find his monthly salary and increment

For the equation 3x − 2𝑦𝑦 = 17, find the value of x when y = −1 and find the value of y when x = 3

A train covered a certain distance at a uniform speed. If the train would have been 6 km/h faster, it would have taken 4 hours less than the scheduled time. And, if the train was slower by 6 km/h it would have taken 6 hours more than the scheduled time. Find the length of the journey.

The difference between a two digit number and the number obtained by interchanging the digits is 27. What is the difference betw een the two digits of the number?

A shopkeeper gives books on rent for reading. She takes a fixed charge for the first two days, and an additional charge for each day thereafter. Latika paid Rs 22 for a book kept for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.

Solve x + 2y = 10 and 2x + y = 14 by substitution method and hence find the value of m for which y = mx + 8.

The sum of two numbers is 45. If 5 is subtracted from each of them, the product of these numbers becomes 124. Find the numbers.

3 chairs and 1 table cost ₹ 900; whereas 5 chairs and 3 tables cost ₹ 2,100. If the cost of 1 chair is ₹ x and the cost of 1 table is ₹ y, then the situation can be represented algebraically as ______.