Express each of the following equations in the form ax+ by + c = 0 and indcate the values of a, b, c in each case.

(i) x = 6

(ii) 3x - y = x - 1

(iii) 2x + 9 = 0

(iv) 4y = 7

(v) x + y = 4

(vi) $\frac{x}{2} - \frac{y}{3} = \frac{1}{6} + y$

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Solution

(i) x = 6
In the form of ax + by + c = 0

we have x + 0y + ( - 6) = 0 where a = 1, b = 0 and c = - 6.

(ii) 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

(iii) 2x + 9 = 0
In the form of ax + by + c = 0 we have 2x + (-1y) + 1 = 0 where a = 2, b = -1 and c = 1

(iv) 4y = 7
In the form of ax + by + c= 0 we have 0x + 4y + (-7) = 0 where a = 0, b = 4 and c = -7

(v) x + y = 4
In the form of ax + by + c = 0 we have 1x + 1y + (-4) = 0 where a = 1, b = 1, c = - 4

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

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

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

2 x - \frac{y}{5} + 6 = 0

(ii) $\frac{x}{5} - \frac{y}{6} = 1$

(iii) $\sqrt{2} x + \sqrt{3} y = 5$

a x + b y + c = 0

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

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 + 5y = 7.5

(ii) $2 x - \frac{y}{5} + 6 = 0$

(iii) 3y - 2x = 6

(iv) 4x = 5y

(v) $\frac{x}{5} - \frac{y}{6} = 1$

(vi) $\sqrt{2} x + \sqrt{3} y = 5$

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