Question

A function becomes $$\dfrac{1}{4}$$, when $$2$$ is subtracted  from the numerator and $$3$$ is added to the denominator. Represent this situation as a linear equation in two variables. Also find two solutions for this.

Solution

$$\cfrac{x-2}{y+3}=\cfrac{1}{4}\\ \Rightarrow 4x-8=y+3\\ \Rightarrow 4x-y=3+8\\ \Rightarrow 4x-y=11\\ \therefore 4x-y-11=0$$ is a linear equation representing $$x$$ and $$y$$ as two variables.Now, When $$x=0, y=-11$$ and when $$y=0$$, $$x=\dfrac{11}{4}$$Hence, $$(0,-11)$$ and $$(\dfrac{11}{4},0)$$ are the two solutions for this equation.Maths

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