Solve the pair of linear equations:

1/2x+1/3y=2

1/3x+1/2y=13/6

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Solution

1/2x + 1/3y = 2
1/3x + 1/2y = 13/6
Let 1/x = p and 1/y = q, then the equations changes as below:
p/2 + q/3 = 2
⇒ 3p + 2q -12 = 0 ... (i)
p/3 + q/2 = 13/6
⇒ 2p + 3q -13 = 0 ... (ii)

By cross-multiplication method, we get

p/-26-(-36) = q/-24-(-39) = 1/9-4
p/10 = q/15 = 1/5
p/10 = 1/5 and q/15 = 1/5
p = 2 and q = 3
1/x = 2 and 1/y = 3
Hence, x = 1/2 and y = 1/3

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Question 1 (i)
Solve the following pairs of equations by reducing them to a pair of linear equations:
$\frac{1}{2 x} + \frac{1}{3 y} = 2$
$\frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}$

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\frac{1}{2 x} + \frac{1}{3 y} = 2, \frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}

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

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\frac{1}{3 x} + \frac{1}{2 y} = \frac{13}{6}

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Solve the pair of linear equations: 1/2x+1/3y=2 1/3x+1/2y=13/6

Solve the pair of linear equations:

1/2x+1/3y=2

1/3x+1/2y=13/6