# NCERT Solutions Class 9 Maths exercise 4.1 and 4.2 -Linear equation in two variable

Here NCERT Solutions Class 9 Maths exercise 4.1 and 4.2 are the solutions of class 9 Maths NCERT textbook exercises 4.1 and 4.2 of chapter 4-Linear equation in two variables are solved for helping class 9 students in their forthcoming exams. All questions are solved by an expert of maths. The exercises 4-1 and 4.2 are easy,so the student will not get any problem to understand the solutions.

**Exercise 4.3-Linear Equation in two Variables**

**NCERT Solutions of class 9 maths**

Chapter 1- Number System | Chapter 9-Areas of parallelogram and triangles |

Chapter 2-Polynomial | Chapter 10-Circles |

Chapter 3- Coordinate Geometry | Chapter 11-Construction |

Chapter 4- Linear equations in two variables | Chapter 12-Heron’s Formula |

Chapter 5- Introduction to Euclid’s Geometry | Chapter 13-Surface Areas and Volumes |

Chapter 6-Lines and Angles | Chapter 14-Statistics |

Chapter 7-Triangles | Chapter 15-Probability |

Chapter 8- Quadrilateral |

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**NCERT Solutions Class 9 Maths exercise 4.1 -Linear equation in two variable**

**Exercise 4.1**

**Q1.The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. **

Ans. Let the cost of the pen is = x and the cost of the notebook is = y

According to question

cost of notebook = 2× Cost of pen

y = 2x

y – 2x = 0

So,the required linear equation in two variable is ,y – 2x = 0

**Q2- Express the following linear equation in the form ax + by + c=0 and indicate the values of a,b and c in each case:**

(iii) -2x + 3y = 6

(iv) x = 3y

(v) 2x = -5y

(vi) 3x +2 = 0

(vii) y-2 =0

(viii) 5 = 2x

Ans. The given equation is

Writting it in the standard form

Comparing it with standard form of linear equation ax + by + c = 0

We have

(ii) We are given the equation

Comparing it with standard form of linear equation ax + by + c = 0

We have

a =1, b = -1/5 and c = -10

(iii) -2x + 3y = 6

Writting it in the standard form ax + by + c = 0

-2x + 3y – 6 = 0

Comparing it with standard form of linear equation ax + by + c = 0

a = -2, b= 3 and c = -6

(iv) x = 3y

Writting it in the standard form ax + by + c = 0

x – 3y +0=0

Comparing it with standard form of linear equation ax + by + c = 0

a =1, b= -3 and c =0

(v) 2x = -5y

Writting it in the standard form ax + by + c = 0

2x + 5y + 0= 0

Comparing it with standard form of linear equation ax + by + c = 0

a = 2, b = 5 and c= 0

(vi) 3x +2 = 0

Writting it in the standard form ax + by + c = 0

3x +0.y + 2 =0

Comparing it with standard form of linear equation ax + by + c = 0

a =3, b=0 and c = 2

(vii) y-2 =0

Writting it in the standard form ax + by + c = 0

0.x + y -2=0

Comparing it with standard form of linear equation ax + by + c = 0

a =0, b=1 and c = -2

(viii) 5 = 2x

Writting it in the standard form ax + by + c = 0

2x +0.y -5= 0

Comparing it with standard form of linear equation ax + by + c = 0

a =2, b= 0 and c= -5

**NCERT Solutions Class 9 Maths exercise 4.1 -Linear equation in two variable**

**Exercise 4.2**

**Q1.Which one of the following options is true ,and why ? y = 3x +5 has**

**(a) A unique solution (ii) Only two solutions (iii) Infinitely many solutions**

Ans.The given equation, y = 3x +5 ,if we put any value of x,we get different corresponding values of y,so for different values of x we get different values of y

Therefore y= 3x +y,has infinite solutions

**Q2. Write four solutions for each of the following equations.**

**(i) 2x + y = 7**

**(ii) πx +y =9**

**(iii) x = 4y**

Ans (i) .The given equation is 2x + y = 7

Putting x = o,we have y =7, for x =1,y=5,for x = 2,y =3, for x =3,y= 1

The four solution of the given equation 2x + y = 7 are tabulated as follows

x | 0 | 1 | 2 | 3 |

y | 7 | 5 | 3 | 1 |

(ii) We are given the equation πx +y =9

For x = 0, y =9, for x=1, 9 -π, for x=2, y = 9-2π, for x = 3, y = 9-3π

The four solution of the given equation 2x + y = 7 are tabulated as follows

x | 0 | 1 | 2 | 3 |

y | 9 | 9 -π | 9 -2π | 9 -3π |

(iii) We are given the equation x = 4y

For x =0,y=0, for x=1, y= 4, for x-2, y= 8,for x=3,y =12

The four solution of the given equation 2x + y = 7 are tabulated as follows

x | 0 | 1 | 2 | 3 |

y | 0 | 4 | 8 | 12 |

**Q3. Check which of the following are solutions of the equation x -2y =4 and which are not:**

**(i) (0,2) (ii) (2,0) (iii) (4,0) (iv) (√2, 4√2) (v) (1,1)**

Ans. Given equation is x -2y =4

(i) Putting x=0 and y = 2 in the equation

0 – 2× 2 = 4

-4 ≠ 4

So, (0,2) is not solution of the given equation

(ii) Putting x =2 and y=0 in the given equation

2 – 2×0 = 4

2 ≠ 4

So, (2,0) is not the solution of the given equation

(iii) Putting x =4 and y=0 in the given equation

4 – 2×0 =4

4 = 4

So, (4,0) is the solution of the given equation

(iv) Putting x =√2 and y = 4√2 in the given equation

√2 – 2× 4√2 = 4

√2 – 8√2 =4

-7√2 ≠ 4

So, (√2, 4√2) is not the solution of the given equation

(v) Putting x =1 and y =1 in the given equation

1- 2×1 = 4

1-2 = 4

-1 ≠ 4

So, (1,1) is not the solution of the given equation

**Q4. Find the value of k, if x =2,y =1 is the solution of equation 2x + 3y = k.**

Ans. Putting the value of x= 2 and y = 1 in the given equation 2x + 3y = k

k= 2×2 + 3× 1

k = 4 + 3

k = 7

Therefore required value of k = 7

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Chapter 7- Permutations and Combinations | Chapter 15- Statistics |

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Chapter 1-Relations and Functions | Chapter 9-Differential Equations |

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Chapter 3-Matrices | Chapter 11 – Three Dimensional Geometry |

Chapter 4-Determinants | Chapter 12-Linear Programming |

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