Which one of the following options is true, and why?
For the equation \(y = 3x + 5\):
(i) a unique solution
(ii) only two solutions
(iii) infinitely many solutions
(iii), because for every value of x, there is a corresponding value of y and vice-versa.
Write four solutions for each of the following equations:
(i) \(2x + y = 7\)
(ii) \(\pi x + y = 9\)
(iii) \(x = 4y\)
(i) (0, 7), (1, 5), (2, 3), (4, -1)
(ii) (1, 9 - \(\pi\)), (0, 9), (-1, 9 + \pi), \(\left(\dfrac{9}{\pi}, 0\right)\)
(iii) (0, 0), (4, 1), (-4, 1), \(\left(2, \dfrac{1}{2}\right)\)
Check which of the following are solutions of the equation \(x - 2y = 4\) and which are not:
(i) (0, 2)
(ii) (2, 0)
(iii) (4, 0)
(iv) \((\sqrt{2}, 4\sqrt{2})\)
(v) (1, 1)
(i) No
(ii) No
(iii) Yes
(iv) No
(v) No
Find the value of k, if \(x = 2, y = 1\) is a solution of the equation \(2x + 3y = k\).
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