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
Test each ordered pair \((x, y)\) by substituting into \(x - 2y = 4\). If the left-hand side equals 4, it is a solution.
(i) \(0 - 2(2) = -4\) ≠ 4, so not a solution.
(ii) \(2 - 2(0) = 2\) ≠ 4, so not a solution.
(iii) \(4 - 2(0) = 4\) matches 4, so this is a solution.
(iv) \(\sqrt{2} - 2(4\sqrt{2}) = \sqrt{2} - 8\sqrt{2} = -7\sqrt{2}\), not 4, so not a solution.
(v) \(1 - 2(1) = -1\) ≠ 4, so not a solution.