Question

Solve the following systems of equations:

$$\begin{gathered} \frac{1}{2x}+\frac{1}{3y}=2 \\ \frac{1}{3x}+\frac{1}{2y}=\frac{13}{6} \end{gathered}$$

Answer 1

The given equations are:

…

…

Multiply equation by and by and subtract equation (ii) from (i) we get

Put the value of in equation, we get
$$\begin{gathered} \frac{1}{2\times {\displaystyle \frac{1}{2}}}+\frac{1}{3y}=2 \\ \frac{1}{3y}=2-1 \\ \frac{1}{3y}=1 \\ y=\frac{1}{3} \end{gathered}$$

Hence the value of and $y=\frac{1}{3}$