# NCERT Solutions For Class 9 Maths Chapter 8 Linear Equations in Two Variables Ex 8.2

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Textbook | NCERT |

Board | CBSE |

Category | NCERT Solutions |

Class | Class 9 |

Subject | Maths |

Chapter | Chapter 8 |

Exercise | Class 9 Chapter 8 Linear Equations in Two Variables Exercise 8.2 |

Number of Questions Solved | 6 |

## NCERT Solutions for Class 9 Maths Chapter 8 Linear Equations in Two Variables Ex 8.2

**NCERT TEXTBOOK EXERCISES**

**Question 1. Which one of the following options is true and why? y = 3x + 5 has**

**(i) a unique solution****(ii) only two solutions****(iii) infinitely many solutions**

**Solution:**

**(iii)** A linear equation in two variables has infinitely many solutions.

**Question 2. Write four solutions for each of the following equations**

**(i) 2x + y = 7****(ii) Ï€x + y = 9****(iii) x = 4y**

**Solution:**

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

By inspection, x = 2 and y = 3 is a solution because for x = 2, y = 3,

2x + y = 2 x 2 + 3 = 4 + 3 = 7

Now, let us choose x = 0 with this value of x, the given equation reduces to y = 7.

So, x = 0, y = 7 is also a solution of 2x + y = 7. Similarly, taking y = 0,

the given equation reduces to 2x = 7 which has the unique solution x = 72 .

So, x = 72 , y = 0 is a solution of 2x + y = 7.

Finally, let us take x = 1

The given equation now reduces to 2 + y = 7 hose solution is given by y = 5.

Therefore, (1, 5) is also a solution of the given equation.

So, four of the infinitely many solutions of the given equation are (2, 3), (0, 7), ( 72 , 0) and (1,5).

**(ii)** Ï€x + y = 9

Now, let us choose x = 0 with this value of x,

the given equation reduces to y = 9 which has a unique solution y = 9.

So, x = 0, y = 9 is also a solution of Ï€x + y = 9

Similarly, taking y = 0, the given equation reduces to x = 9/Ï€ So, x = 9/Ï€ ,y = 0 is a solution of Ï€x + y = 9 as well.

Finally, let us take x = 7 the given equation now reduces to 22/7 . 7 + y = 9

whose solution is given by y = -13.

Therefore; (7,-13) is also a solution of the given equation.

So, four of the infinitely many solutions of the given equation are

**(iii)** x = 4y â‡’ x â€“ 4y = 0

By inspection, x = 0, y = 0 is a solution because for x = y = 0, 0 â€“ 4 x 0 = 0 â€“ 0 = 0, it satisfies.

Now, let us choose x = 4 with this value of x,

the given equation reduces to y = 1 which has a unique solution y = 1.

So, x = 4, y = 1 is also a solution , of x â€“ 4y = 0. Similarly, taking y = 1/2 , the given equation reduces to x = 2.

So , x = 2, y = 1/2 is a solution x â€“ 4y = 0 as well.

Finally, let us take x = 1, the given equation now reduces to 1 â€“ 4y = 0

whose solution is given by y = 1/4. Therefore, (1,1/4) is also a solution of the given equation. So, four

of the infinitely many solutions of the given equation are

**Question 3. Check which of the following are solution of the equation x â€“ 2y = 4 and which are not?**

**(i) (0, 2)****(ii) (2,0)****(iii) (4,0)****(iv) (âˆš2,4âˆš2)****(v) (1,1)**

**Solution:**

**(i)** Take x â€“ 2y and put x = 0, y = 2,

we get 0 â€“ 2 x 2 = 0 â€“ 4 = -4 â‰ 4

Hence, (0, 2) is not a solution of x â€“ 2y = 4.**(ii)** Take x â€“ 2y and put x = 2, y = 0,

we get 2 â€“ 2 x 0 = 2 â€“ 0 = 2 â‰ 4

Hence, (2, 0) is not a solution of x â€“ 2y = 4.

**Take x â€“ 2y and put x = 4, y = 0;**

(iii)

(iii)

we get 4 â€“ 2 x 0 = 4 â€“ 0 = 4

Hence, (4, 0) is a solution of x â€“ 2y = 4.

**Take x â€“ 2y and put x = âˆš2, y = 4âˆš2, we get**

(iv)

(iv)

âˆš2 â€“ 2 x 4âˆš2 = âˆš2 â€“ 8âˆš2 =-7âˆš2 â‰ 4

Hence, (âˆš2,4âˆš2) is not a solution of x â€“ 2y = 4

**Take x â€“ 2y and put x = 1, y = 1,**

(v)

(v)

we get 1 â€“ 2 x 1 = 1 â€“ 2 = -1 â‰ 4

Hence, (1,1) is not a solution of x â€“ 2y = 4.

**Question 4. Find the value of k, if x = 2, y = 1 is a solution of the equation 2x + 3 y = k.**

**Solution:**

Take 2x + 3y = k

Put x = 2, y = 1 then we get, 2 x 2 + 3 x 1 = k

â‡’ 4 + 3 = k

â‡’ k = 7

## NCERT Solutions for Class 9 Maths Chapter 8 Linear Equations in Two Variables Exercise 8.2 PDF

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