Express each of the following equations in the form ax+ by + c = 0 and indicate the values of a, b, c in each case.
(i) 3x - y = x - 1
(ii) $\frac{x}{2} - \frac{y}{3} = \frac{1}{6} + y$

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Solution

(i) 3x – y = x – 1
In the form of ax + by + c = 0 we have 2x + (-1y) + 1 = 0 where a = 2, b = -1 and c = 1

(ii) $\frac{x}{2} - \frac{y}{3} = \frac{1}{6} + y M u l t i p l y t h r o u g h o u t w i t h 6 3 x - 2 y = 1 + 6 y \Rightarrow 3 x - 8 y + (- 1) = 0 a x + b y + c = 0 a = 3, b = - 8, c = - 1$

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\frac{x}{2} - \frac{y}{3} = \frac{1}{6} + y

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