NCERT Class 9 Solutions: Linear Equation in Two Variable (Chapter 4) Exercise 4.2 – Part 1

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Linear equation

Give linear equation for y=3x-4

Give Linear Equation Like Y =Mx+C

Give linear equation for y=3x-4

Q-1 Which one of the following option is true, and why?

y=3x+5 has

  1. A unique solution

  2. Only two solution

  3. Infinitely many solutions

Solution:

  • Infinitely many solutions

  • Because a linear equation in two variables has infinitely many solutions. We keep changing the value of x and solve the linear equation for the corresponding value of y .

Q-2 Write four solutions for each of the following equations:

  1. 2x+y=7

  2. πx+y=9

  3. x=4y

Solution:

i) 2x+y=7

For x=1 ,

2(1)+y=7

y=5

Therefore, (1,5) is a solution of this equation.

For x=2 ,

2(2)+y=7

y=3

Therefore, (2,3) is a solution of this equation.

For x=3 ,

2(3)+y=7

y=1

Therefore, (3,1) is a solution of this equation.

For x=4 ,

2(4)+y=7

y=1

Therefore, (4,1) is a solution of this equation.

Four solutions of 2x+y=7 is (1,5),(2,3) , (3,1),(4,1)

ii) πx+y=9

For x=1π

π(1π)+y=9

y=9

Therefore, (1π,9) is a solution of this equation.

For x=2π ,

π(2π)+y=9

y=7

Therefore, (2π,7) is a solution of this equation.

For x=3π ,

π(3π)+y=9

y=6

Therefore, (3π,6) is a solution of this equation.

For x=4π,

π(4π)+y=9

y=5

Therefore, (4π,5) is a solution of this equation.

Four solution of πx+y=9 (1π,9),(2π,7),(3π,6),(4π,5)

iii) x=4y

For x=8 ,

8=4y

y=2

Therefore, (8,2) is a solution of this equation.

For x=12,

12=4y=3

Therefore, (12,3) is a solution of this equation.

For x=16,

16=4y

y=4

Therefore, (16,4) is a solution of this equation.

For x=20,

20=4y

y=5

Therefore , (20,5) is a solution of this equation.

Four solution of x=4y is (8,2),(12,3),(16,4),(20,5)

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