Question

1/7x+1/6y=3 1/2x+1/3y=5.solve for x and y

Answer 1

Given that;

Eq1:

$\frac{1}{7x} + \frac{1}{6y} = 3$

let 1/x = a & 1/y = b

$\frac{a}{7} + \frac{b}{6} = 3$

$\frac{6a + 7b}{42} = 3$

$6a \: + 7b \: = 126 \: ..........(3)$

Eq2:

$\frac{1}{2x} + \frac{1}{3y} = 5$

let 1/x = a & 1/y = b

$\frac{a}{2} + \frac{b}{3} = 5$

$\frac{3a + 2b}{6} = 5$

$3a \: + 2b \: = 30...........(4)$

From (3) - 2×(4) ;

• 7b-4b = 126-60
• 3b = 66
• b = 22.

From substituting value of b in (4);

• 3a +2(22) = 30
• 3a = 30 - 44
• 3a = 14
• a = 14/3

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