The linear equations of $\frac{4}{x-1}+ \frac{5}{y+2}=16$ and $\frac{9}{x-1}+ \frac{7}{y+2}=20$ is________________ and _______________.

Given Equations :  $\frac{4}{x-1}+ \frac{5}{y+2}=16$ and $\frac{9}{x-1}+ \frac{7}{y+2}=20$ 

Let's solve the equations step-by-step

$\frac{4}{x-1}+ \frac{5}{y+2}=16$  

$4\left[\frac{1}{x-1}\right]+5\left[\frac{1}{y+2}\right]=16----------------1$

$\frac{9}{x-1}+ \frac{7}{y+2}=20$

$9\left[\frac{1}{x-1}\right]+7\left[\frac{1}{y+2}\right]=20----------------2$

Now substitute $\left[\frac{1}{x-1}\right] and \left[\frac{1}{y+2}\right]$ by any of the variables let's take r and s 

i.e. $4r+5s=16----------------3$

$9r+7s=20----------------4$

3 and 4 are the linear equations of  $\frac{4}{x-1}+ \frac{5}{y+2}=16$ and $\frac{9}{x-1}+ \frac{7}{y+2}=20$.