Solve for x and y: 2x+5y xy =6, 4x-5y xy =-3 - Vidyadip

Question

Solve for $x$ and $y$:
$\frac{\text{2x}+\text{5y}}{\text{xy}}=6,$
$\frac{\text{4x}-\text{5y}}{\text{xy}}=-3$

✓

Answer

The given equations are:
$\frac{\text{2x}+\text{5y}}{\text{xy}}=6$
$\Rightarrow\frac{2}{\text{y}}+\frac{5}{\text{x}}=6\ \dots(\text{i})$
$\frac{\text{4x}-\text{5y}}{\text{xy}}=-3$
$\Rightarrow\frac{4}{\text{y}}-\frac{5}{\text{x}}=-3\ \dots(\text{ii})$
Adding $(i)$ and $(ii),$ we get
$\frac{6}{\text{y}}=3$
$\Rightarrow\text{y}=2$
Substituting $y = 2$ in $(i)$, we get $x = 1$
Hence, $x = 1$ and $y = 2$

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