Question

Solve the following equations 5/x-1+1/y-2=2 6/x-1-3/y-2=1

Answer 1

i hope it will help you

Answer 2

Answer:

The solution of the equation is x=4 and y=5.  

Step-by-step explanation:

Given : Equations $\frac{5}{x-1}+\frac{1}{y-2}=2$ and $\frac{6}{x-1}-\frac{3}{y-2}=1$

To find : Solve the following equation ?

Solution :

For simpler calculation,

Put $X=\frac{1}{x-1}$ and $Y=\frac{1}{y-2}$

Now, Substitute in the given equations,

$\frac{5}{x-1}+\frac{1}{y-2}=2$....(1)

$5X+Y=2$ .....(3)

$\frac{6}{x-1}-\frac{3}{y-2}=1$ .....(2)

$6X-3Y=1$......(4)

Solving (3) and (4),

Multiply equation (3) by 3 and add (4) from it,

$15X+3Y+6X-3Y=6+1$

$21X=7$

$X=\frac{7}{21}=\frac{1}{3}$

Substitute in (3),

$5(\frac{1}{3})+Y=2$

$\frac{5}{3}+Y=2$

$Y=2-\frac{5}{3}$

$Y=\frac{1}{3}$

Substitute in the condition,

$X=\frac{1}{x-1}$

$\frac{1}{3}=\frac{1}{x-1}$

$x-1=3$

$x=4$

and  $Y=\frac{1}{y-2}$

$\frac{1}{3}=\frac{1}{y-2}$

$y-2=3$

$y=5$

Therefore, The solution of the equation is x=4 and y=5.