NCERT Solutions For Class 9 Math Chapter – 4 Exercise – 4.2

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NCERT Solutions For Class 9 Math Chapter – 4 Exercise – 4.2

 

Q1. Which one of the following options is true , and why ?

Y = 3x + 5

  • Unique solution   (ii) only two solutions   (iii) infinitely many solutions

Solution:-

x 0 1 2 …. 100
y, where y=3x+5 5 8 11 …. 305

Infinitely many solutions.

 

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

  • 2x + y = 7   (ii)  ∏x + y = 9  (iii) x = 4y

Solution:-

 

  • 2x + y = 7

Y = 7 – 2x

Put x = 0

Y = 7 – 0

Y = 7

(0,7) is the solution.

 

Put x = 1

Y = 7 – 2 x 1

Y = 5

(1,5) is the solution

 

Put x = 2

Y = 7 – 2 x 2

Y = 3

(2,3) is the solution

 

Put x = -1

Y = 7 –  2 (-1)

Y = 9

(-1,9) is the solution.

 

 

The four solution of the equation 2x + y = 7 are (0,7) , (1,5) (2,3) and (-1,9)

 

  • ∏x + y= 9

Y = 9 – ∏x

X = 0

Y = 9 – ∏ x 0

Y = 9

(0,9) is the solution.

 

Put x = 1

Y = 9 – ∏ x 1

Y= 9 – ∏

(1,9-∏)  is the solution.

Put x =  2

Y = 9 – ∏ x 2

Y = 9 – 2∏

(2,9-2∏) is the solution.

 

Put x = -1

Y = 9 – ∏ x (-1)

Y = 9 + ∏

(-1 , 9 + ∏) is the solution.

 

The four solutions of the equation ∏x +  y = 9 are (0,9) (1, 9-∏) , (1, 9 – 2∏) and (-1,9+∏).

 

  • X = 4y

X = 0

0 = 4y

y = 0

(0,0) is the solution.

Put x = 1

1 = 4y

Y = 1/4

(1.1/4 ) is the solution.

 

Put x = 4

4 = 4y

Y = 1

(4,1) is the solution.

 

Put x = 8

8 = 4y

Y = 2

(8,2) is the solution.

 

The four solutions of the equation ∏x + y = 9 are (0,0) , (1.1/4) , (4,1) and (8,2).

 

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

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

Solution:-

 

  • X = 0

Y = 2

0-2×2 = 4

-4 ≠ 4

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

 

  • X = 2

Y = 0

2 -2×0 = 4

2 ≠ 4

(2,0) is not a solution of the give equation.

 

  • X = 4

Y = 0

 

4-2×0= 4

4 = 4

(4,0) is a solution of the given equation.

 

  • X = √2

Y = 4√2

√2 – 2 x 4√2 = 4

√2(1-8) = 4

= -7√2 ≠ 4

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

 

  • X = 1

Y = 1

1 – 2×1 = 4

-1 ≠ 4

(1,1)  is not a solution of the given equation.

 

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

Solution:-

 

2x + 3y = k

X = 2 y = 1

2 x 2 + 3 x 1 = k

K = 4 + 3

K = 7