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Question 22
If $$(\frac{x}{a}) + (\frac{y}{b}) = 3$$ and $$(\frac{x}{b}) - (\frac{y}{a}) = 9$$, then what is the value of $$\frac{x}{y}$$?
Solution
$$(\frac{x}{a}) + (\frac{y}{b}) = 3$$
bx+ay=3ab
3bx+3ay=9ab
$$(\frac{x}{b}) - (\frac{y}{a}) = 9$$
ax-by=9ab
3bx+3ay=ax-by
3bx-ax=-by-3ay
x(3b-a)=y(-b-3a)
y/x =(a-3b)/(3a+b)
x/y=(3a+b)(a-3b)
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