​ Solve the following systems of equations: 5/(x - 1)+ 1/(y - 2) = 2 6/(x - 1) - 3/(y - 2) = 1 ​

Question

Solve the following systems of equations:

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

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

Answer 1

Given:

The system of equations:

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

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

To find:

The values of x and y

Solution:

Let

 

Now system of equations become:

5u + v = 2 ....... (1)

6u - 3v = 1 ....... (2)

Now multiply equation (1) by 3 and add to equation (2),3(5u + v)+ 6u - 3v = 3(2) +115u +3v + 6u - 3v = 6+121u = 7

⇒x - 1 =3

⇒x = 3 + 1

⇒x = 4

Now put u = \(\frac{1}{3}\) in the equation (1) to get v,

⇒y - 2 = 3

⇒y = 3 + 2

⇒y = 5

Hence the values are

x = 4 and y = 5.