If 4x + 6y = 3xy and 8x + 9y = 5xy then

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x = 3, y = 4 Explanation: From 4x + 6y = 3xy $\Rightarrow$ x(3y – 4) = 6y $\Rightarrow$ x = (6y)/(3y - 4) From 8x + 9y = 5xy $\Rightarrow$ x(5y – 8) = 9y $\Rightarrow$ x = (9y)/(5y - 8) Equate the two expressions and cancel y $\neq$ 0: 6(5y – 8) = 9(3y – 4) $\Rightarrow$ 30y – 48 = 27y – 36 $\Rightarrow$ 3y = 12 $\Rightarrow$ y = 4 Then x = (6 xx 4)/(3 xx 4 - 4) = $\frac{24}{8}$ = 3

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