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Question

$$\dfrac{2x}{a}+\dfrac{y}{b}=2$$
$$\dfrac{x}{a}-\dfrac{y}{b}=4$$.


Solution

We are givenm
$$\dfrac {2x}{a}+\dfrac {y}{b}=2---(1)$$
$$\dfrac {x}{a}-\dfrac {y}{b}=4---(2)$$
Now, odd equation $$(1)$$ with equation $$(2)$$ we get
$$\dfrac {3x}{a}=6\ \Rightarrow \boxed {x=2a}$$ or $$\boxed {a=\dfrac {x}{2}}$$
now put $$x=2a$$ in the equation $$(1)$$ 
we get,
$$\dfrac {2(2a)}{a}+\dfrac {y}{b}=2\ \Rightarrow \dfrac {y}{b}=2-4=-2$$
$$\boxed {y=-2b}$$ or $$\boxed {b=\dfrac {-y}{2}}$$
$$(x, y)=(2a-2b)$$ or 
$$(a, b)=\left (\dfrac {x}{2}, \dfrac {-y}{2}\right)$$

Mathematics

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