Write two solutions for each of the following equations:
Question:

Write two solutions for each of the following equations:

(i) 5x – 2y = 7 

(ii) x = 6y 

(iii)  x + πy = 4 

(iv) (2/3)x – y = 4. 

Solution:

(i) We are given,

3x + 4y = 7

Substituting x = 1

In the given equation, We get

3 ×1 + 4y = 7

4y = 7- 3 – 4 = 4Y

Y = 1

Thus x = 1 and y = 1 is the solution of 3x + 4y = 7

Substituting x = 2 in the given equation, we get

3× 2 + 4y = 7

4y = 7 – 6

y = 1/4

Thus x = 2 and y = 1/4 is the solution of 3x + 4y = 7 
(ii) We are given, x = 6y

Substituting x = 0 in the given equation, we get 0 = 6y

6 y = 0

y = 0

Thus x = 0, ⟹ Solution (0, 0)

Substituting x = 6

6 = 6y

y = 6/6

y = 1

⟹ Solution (6, 1) 

(iii) We are given x + πy = 4 

Substituting x = 0 in the given equation,

We get 0 + πy = 4 

πy = 4

y = 4/π 

⟹ Solution = (0, 4/π)

Substituting y = 0 in the given equation, we get x + 0 = 4

x = 4

⟹ Solution = (4, 0)
(iv) We are given (2/3) x – y = 4 

Substituting x = 0 in the given equation, we get 0 – y = 4

y = – 4

Thus x = 0 and y = – 4 is a solution

Substituting x = 3 in the given equation, we get (2/3) × 3 − y = 4 

2 – y = 4

y = 2 – 4

y = -2

Thus x = 3 and y = – 2 is a solution 

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