Question

x/7+y/3=5;x/2-y/9=6 by subsitution method

Answer 1

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Answer 2

Answer:

$x = 14 , \: y = 9$

Step-by-step explanation:

$Given\:pair\:of\: equations:\\\frac{x}{7}+\frac{y}{3}=5$

$\implies \frac{y}{3}=5-\frac{x}{7}\:---(1)$

$and\:\frac{x}{2}-\frac{y}{9}=6$

$\implies \frac{x}{2}-\frac{y}{3}\times \frac{1}{3}=6\:---(2)$

$substitute \:(1)\:in \: equation\:(2),\: we\:get$

$\implies \frac{x}{2}-(5-\frac{x}{7})\times \frac{1}{3}=6\:---(2)$

$\implies \frac{x}{2}-\frac{5}{3}+\frac{x}{21}=6$

$\implies \frac{x}{2}+\frac{x}{21}=6+\frac{5}{3}$

$\implies \frac{21x+2x}{42}=\frac{18+5}{3}$

$\implies \frac{23x}{42}=\frac{21}{3}$

$\implies x = \frac{23}{3}\times \frac{42}{23}$

$\implies x = 14\:--(3)$

$put \: x=14 \: in \: equation \:(1),\\we\:get$

$\frac{y}{3}=5-\frac{14}{7}$

$\implies \frac{y}{3}=5-2$

$\implies y = 3\times 3 = 9$

Therefore,

$x = 14 , \: y = 9$

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