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), \(\left(2, \dfrac{1}{2}\right)\)
For each equation, pick convenient \(x\) values and solve for \(y\), or pick \(y\) and solve for \(x\). Each ordered pair that satisfies the equation is a valid solution.
Example for \(2x + y = 7\): if \(x = 0\) then \(y = 7\); if \(x = 1\) then \(2(1) + y = 7\) so \(y = 5\); if \(x = 2\) then \(y = 3\); if \(x = 4\) then \(y = -1\). Similar substitutions generate the listed pairs for the other equations.