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.
(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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