Question

Solve by using cross multiplication method.5/x-1+1/y-2 =2 6/x-1 3/y-2 =1​

Answer 1

The answer is $x = \frac{14}{5} , y = \frac{5}{7}$

Step-by-step explanation:

Since we have to solve the given pair of equations by cross multiplication, let us consider

$\frac{1}{x-1} = a , \frac{1}{y-2} = b$

Then the equations become

$5a + b = 2 \\6a + 3b = 1$

Multiply the first equation by 3 , second equation by 1 and adding both the equations we get,

$15a + 3b = 6\\6a + 3b = 1$

changing the signs of each term and cancelling the $b$ value we get,

$9a = 5$

$a = \frac{5}{9}$

subsituting the $a$ value in any one of the above two equations we get

$5(\frac{5}{9} ) +b = 2\\\frac{25}{9} + b = 2\\ b = 2 - \frac{25}{9}\\ b = \frac{18 - 25}{9} \\b = \frac{-7}{9}$

Therefore

$x-1 = \frac{1}{a}\\ x - 1 = \frac{9}{5}\\ x = \frac{9}{5} + 1\\x = \frac{14}{5}$

and

$y-2 = \frac{9}{-7}\\ y = \frac{-9}{7} + 2\\y = \frac{5}{7}$

Hence $x = \frac{14}{5} , y = \frac{5}{7}$

Answer 2

x = 4 and y = 5 is solution!

Step-by-step explanation:

Given,  5 / (x - 1) + 1 / (y - 2) = 2 '''''''''''(1)

& 6 / (x - 1) - 3 / (y - 2) = 1 ''''''''''''''''''(2)

Let 1/ (x - 1) = u and 1 / (y - 2) = v ''''''''''''''(A)

Now, Equation (1) and (2) changes to -  

5u + v = 2 '''''''''''(3)

6u - 3v = 1 '''''''''(4)

From equation (3) we get -

5u + v = 2 or v = 2 - 5u  

Now, Putting the value of v in equation (4) we get -

6u - 3v = 1

⇒ 6u - 3(2 - 5u) = 1

⇒ 6u - 6 + 15u = 1

⇒21u = 1 + 6

⇒ u = 7/21 Hence, u = 1/3

Putting value of u in equation (3) we get -  

5u + v = 2

⇒ v = 2 - 5/3

⇒ v = (6 - 5)/3 or v = 1/3

Now, applying these values in (A) we get x and y as -  

u = 1 / (x - 1)

or 1/3 = 1/ (x -1) whose reciprocals gives-  

x - 1 = 3 or x = 4.

Similarly, the value of y has been calculated as y = 5.

Hence, x = 4 and y = 5 is solution for the given equations.