Write four solutions for each of the following equations:
(i) 2x + y = 7
(ii) πx + y = 9
(iii) x = 4y

Solution:

In the given  Linear equations, we can find any number of solutions by putting different values of x and obtain different values of y.

i) 2x + y = 7

Changing the subject of the equation to y, and solving, we get,

∴ y = 7 - 2x  

Let us now take different values of x and substitute them in the given equation.

For x = 0, we get y = 7 - 2 (0) ⇒ y = 7. Hence, we get ( x, y ) = (0, 7) 

For x = 1, we get y = 7 - 2 (1) ⇒ y = 5. Hence, we get ( x, y ) = (1, 5)

For x = 2, we get y = 7 - 2(2) ⇒ y = 3. Hence, we get ( x, y ) = (2, 3).

For x = 3, we get y = 7 - 2(3) ⇒ y = 1. Hence, we get ( x, y ) = (3, 1).

Therefore, four solutions of the given equation are (0, 7), (1, 5), (2, 3) and (3, 1).

ii) πx + y = 9

∴ y = 9 - πx  

Let us now take different values of x and substitute them in the given equation.

For x = 0, y = 9 - π(0) ⇒ y = 9. Hence, we get ( x, y) = (0, 9)

For x = 1, y = 9 - π(1) ⇒ 9 - π. Hence, we get ( x, y) = (1, 9 - π)

For x = 2, y = 9 - π(2) ⇒ 9 - 2π. Hence, we get ( x, y) = (2, 9 - 2π)

For x = 3, y = 9 - π(3) ⇒ 9 - 3π. Hence, we get ( x, y) = (3, 9 - 3π)

Therefore, four solutions of the given equation are (0, 9), (1, 9 - π), ( 2, 9 - 2π) and (3, 9 - 3π).

iii) x = 4y

∴ y = x/4  

Let us now take different values of x and substitute them in the given equation.

For x = 0, y = 0/4 = 0. Hence, we get (x, y) = (0, 0)

For x = 1, y = 1/4. Hence, we get (x, y) = (1, 1/4)

For x = 2, y = 2/4 = 1/2. Hence, we get (x, y) = (2, 1/2)

For x = 3, y = 3/4. Hence, we get (x, y) = (3, 3/4)

Therefore, four solutions of the given equation are (0, 0), (1, 1/4), (2, 1/2) and (3, 3/4).

☛ Check: NCERT Solutions Maths Class 9 Chapter 4

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Video Solution:

Write four solutions for each of the following equations: (i) 2x + y = 7 (ii) πx + y = 9 (iii) x = 4y

NCERT Solutions Class 9 Maths Chapter 4 Exercise 4.2 Question 2

Summary:

Four solutions for each of the following equations 2x + y = 7, πx + y = 9 and x = 4y are {(0,7), (1,5), (2,3), (3,1)}, {(0,9), (1, 9-π), (2, 9−2π), (3, 9−3π)} and {(0,0), (1,1/4), (2,1/2), (3,3/4)} respectively.

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