Question

# Solve for x and y: $\frac{x}{2}-\frac{y}{9}=6\phantom{\rule{0ex}{0ex}}\frac{x}{7}+\frac{y}{3}=5\phantom{\rule{0ex}{0ex}}$ −117 y=−1

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Solution

## The given system of equations can be written as $9x-2y=108.....\left(i\right)\phantom{\rule{0ex}{0ex}}3x+7y=105.....\left(ii\right)$ Multiplying (i) by 7 and (ii) by 2, we get $63x+6x=108×7+105×2\phantom{\rule{0ex}{0ex}}⇒69x=966\phantom{\rule{0ex}{0ex}}⇒x=\frac{966}{69}=14$ Now, substituting x = 14 in (1), we have $9×14-2y=108\phantom{\rule{0ex}{0ex}}⇒2y=126-108\phantom{\rule{0ex}{0ex}}⇒y=\frac{18}{2}=9$ Hence, x = 14 and y = 9.

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