Question

solve for x and y .2/x-1+3/y-2=1 and 5/x-1+6/y-2=7​

Answer 1

$\bf\underline{\underline{\green{SOLUTION:-}}}$

Given

• 2/x-1 + 3/y-2 =1
• 5/x-1 + 6/y-2 =7

To Calculate

• Value of x and y

Step by step explanation

• 2/x-1 + 3/y-2 =1____________(1)
• 5/x-1 + 6/y-2 =7____________(2)

$= \: \frac{2}{x - 1} + \frac{3}{y - 2} = 1$

Let 1/x-1 = u And 1/y-2 = v

2u +3v=1____________(3)

$= \: \frac{5}{x - 1} + \frac{6}{y - 2} = 7$

= 5u+6v=7_________(4)

On Multiply eq3 by 2

2(2u+3v=1)

⟹ 4u+6v=2_____________(5)

On subtracting eq5 from 4

5u+6v=7

4u+6v=2

__________

v= 5

__________

Putting value of v in eq 5

4u+6v=2

⟹4u+6×5=2

⟹4u+30=2

⟹ 4u = 2-30

⟹ 4u = -28

⟹ u= -28/4

⟹ u= -7

1/x-1 = u

$⟹ \: \frac{1}{x - 1} = - 7$

$= \frac{1}{x - 1} = \frac{ - 7}{1} \\ \\ = 7(x - 1) = 1 \\ \\ = 7x - 7 = 1 \\ \\ = 7x = 1 + 7 \\ \\ = 7x = 8 \\ \\ = x = \frac{8}{7}$

1/y-2 = v

$= \frac{1}{y - 2} = \frac{5}{1}$

$= 5(y - 2) = 1 \\ \\ = 5y - 10 = 1 \\ \\ = 5y = 1 + 10 \\ \\ = 5y = 11 \\ \\ = y = \frac{11}{5}$

$\bf\underline{\underline{\green{HENCE:-}}}$

• x= 8/7
• y= 11/5

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