#### Chapters

Chapter 2: Real Numbers

Chapter 3: Polynomials

Chapter 4: Ratio and Proportion

Chapter 5: Linear Equations in Two Variables

Chapter 6: Financial Planning

Chapter 7: Statistics

## Chapter 5: Linear Equations in Two Variables

#### Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 5 Linear Equations in Two Variables Exercise Practice Set 5.1 [Page 86]

By using variables *x* and *y *form any five linear equations in two variables.

Write five solutions of the equation *x *+* y* = 7.

Solve the following sets of simultaneous equations.

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

Solve the following sets of simultaneous equations.

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

Solve the following sets of simultaneous equations.

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

Solve the following sets of simultaneous equations.

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

Solve the following sets of simultaneous equations.

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

Solve the following sets of simultaneous equations.

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

#### Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 5 Linear Equations in Two Variables Exercise Practice Set 5.2 [Page 90]

In an envelope there are some 5 rupee notes and some 10 rupee notes. Total amount of these notes together is 350 rupees. Number of 5 rupee notes are less by 10 than number of 10 rupee notes. Then find the number of 5 rupee and 10 rupee notes.

The denominator of a fraction is 1 more than twice its numerator. If 1 is added to numerator and denominator respectively, the ratio of numerator to denominator is 1 : 2. Find the fraction.

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 total number of lions and peacocks in a certain zoo is 50. The total number of their legs is140. Then find the number of lions and peacocks in the zoo.

Sanjay gets fixed monthly income. Every year there is a certain increment in his salary. After 4 years, his monthly salary was Rs. 4500 and after 10 years his monthly salary became 5400 rupees, then find his original salary and yearly increment.

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.

The sum of the digits in a two-digits number is 9. The number obtained by interchanging the digits exceeds the original number by 27. Find the two-digit number.

In ΔABC, the measure of angle A is equal to the sum of the measures of ∠B and ∠C. Also the ratio of measures of ∠B and ∠C is 4 : 5. Then find the measures of angles of the triangle.

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.

In a competitive examination, there were 60 questions. The correct answer would carry 2 marks, and for incorrect answer 1 mark would be subtracted. Yashwant had attempted all the questions and he got total 90 marks. Then how many questions he got wrong ?

#### Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra Chapter 5 Linear Equations in Two Variables Exercise Problem Set 5 [Pages 91 - 92]

Choose the correct alternative answers for the following questions.

If 3x + 5y = 9 and 5x + 3y= 7 then What is the value of x + y ?

2

16

9

7

Choose the correct alternative answers for the following questions.

'When 5 is subtracted from length and breadth of the rectangle, the perimeter becomes 26.' What is the mathematical form of the statement ?

*x -**y*= 8x + y = 8

x + y = 23

2x + y = 21

Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay's age ?

20

15

10

5

Solve the following simultaneous equations.

x - 2 y = -1 ; 2x - y = 7

Solve the following simultaneous equations.

x + y = 11 ; 2x - 3 y = 7

Solve the following simultaneous equations.

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

Solve the following simultaneous equations.

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

Solve the following simultaneous equations.

x - 2y = - 2 ; x + 2y = 10

By equating coefficients of variables, solve the following equations.

3x - 4y = 7; 5x + 2y = 3

By equating coefficients of variables, solve the following equations.

5x + 7 y = 17 ; 3x - 2y = 4

By equating coefficients of variables, solve the following equations.

x - 2y = -10 ; 3x - 5y = -12

By equating coefficients of variables, solve the following equations.

4x + y = 34 ; x + 4y = 16

Solve the following simultaneous equations.

`x/3 + y/4 = 4` ; `x/2 - y/4 = 1`

Solve the following simultaneous equations

`x/3 + 5y = 13 ; 2x + y/2 = 19`

Solve the following simultaneous equations.

`2/x + 3/y = 13` ; `5/x - 4/y = -2`

A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.

The total cost of 6 books and 7 pens is 79 rupees and the total cost of 7 books and 5 pens is 77 rupeess. Find the cost of 1 book and 2 pens.

The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves rupees 200, find the income of each.

If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 8 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.

The distance between two places A and B on road is 70 kilometers. A car starts from A and the other from B. If they travel in the same direction, they will meet after 7 hours. If they travel towards each other they will meet after 1 hour, then find their speeds.

The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.

## Chapter 5: Linear Equations in Two Variables

## Balbharati solutions for Maharashtra state board Class 9 Mathematics 1 Algebra chapter 5 - Linear Equations in Two Variables

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Concepts covered in Maharashtra state board Class 9 Mathematics 1 Algebra chapter 5 Linear Equations in Two Variables are Concept of Linear Equations in Two Variables, Elimination Method, General Form of Linear Equation in Two Variables, Substitution Method.

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