Question

Solve the following equations:-
x/7 + y/3 = 5
x/2 - y/9 = 6

Answer 1

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$\frac{x}{7} + \frac{y}{3} = 5 \\ Taking \: l.c.m \\ = > \frac{3x + 7y}{21} = 5 \\ = > 3x + 7y = 105 ----->(i) \\ \\ \frac{x}{2} - \frac{y}{9} = 6 \\ Taking \: l.c.m \\ \\ = > \frac{9x - 2y}{18} = 6 \\ \\ = > 9x - 2y = 108 ----> (ii) \\ \\ Now ,\: Using \: Substitution \: method : \\ From \: eq.(i) \\ \\ = > 3x + 7y = 105 \\ = > x = \frac{105 - 7y}{3} ----> (iii) \\ \\ Putting \: the \: value \: of \: x \: in \: eq.(ii) \\ \\ = > 9x - 2y = 108 \\ \\ = > 9 ( \frac{105 - 7y}{3} ) - 2y = 108 \\ \\ = > 945 - 63y - 6y = 324 \\ \\ = > - 69y = 324 - 945 \\ \\ = > - 69y = - 621 \\ \\ = > y = 9 \\ \\ Putting \: y = 9 \: in \: eq.(3) \\ \\ = > x = \frac{105 - 7y}{3} \\ \\ = > x = \frac{105 - 7(9)}{3} \\ \\ = > \frac{105 - 63}{3} \\ \\ = > x = \frac{42}{3} \\ \\ = > x =13$

So , The value of 'x' is 13 and 'y' is 9 .....
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