Question

A function becomes $\frac{1}{4}$, 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.

Answer 1

$\frac{x-2}{y+3}=\frac{1}{4}\Rightarrow 4x-8=y+3\Rightarrow 4x-y=3+8\Rightarrow 4x-y=11\therefore 4x-y-11=0$

is a linear equation representing $x$ and $y$ as two variables.

Now,

When $x=0,y=-11$ and when $y=0$, $x=\frac{11}{4}$

Hence, $(0,-11)$ and $(\frac{11}{4},0)$ are the two solutions for this equation.