Question

Solve the following pair of equations
$\frac{4}{x}+3y=8;\frac{6}{x}-4y=-5$

Answer 1

$\begin{array}{c}\Rightarrow \frac{4}{x}+3y=\mathrm{8........}\left(1\right)\\ \Rightarrow \frac{6}{x}-4y=-5\\ \Rightarrow -4y=\frac{\left(-5-6\right)}{x}\\ \Rightarrow y=\frac{\left(5x+6\right)}{4x}..........\left(2\right)\\ now,substitutingvalueofyinequation\left(1\right)\\ \Rightarrow \frac{4}{x}+\frac{3\left(5x+6\right)}{4x}=8\\ \Rightarrow \frac{\left(16+15x+18\right)}{4x}=8\\ \Rightarrow 34+15x=32x\\ \Rightarrow 34=17x\\ \Rightarrow x=2\\ now,substiutingxinequation\left(2\right)\\ \Rightarrow y=\frac{\left(5x+6\right)}{4x}\\ \Rightarrow y=\left(\frac{10+6}{8}\right)\\ \Rightarrow y=\frac{16}{8}\\ \Rightarrow y=2\\ therefore,\\ x=y=2\end{array}$