Question

4/x+1+7/y+2=2 and 10/x+1+14/y+2=9/2, x≠-1,y≠-2,Solve the given pair of equations.

Answer 1

By solving above equations according to given below.

Answer 2

Dear student,

Answer: x= 3 , y = 5

Solution:

$\frac{4}{x+1} +\frac{7}{y+2} =2 \\\\ \frac{10}{x+1} +\frac{14}{y+2} =\frac{9}{2}$

let 1/(x+1) = u and 1/(y+2) = v

4u+7v = 2 .......eq1

10u+14v = 9/2

20 u+ 28 v = 9 ......eq2

Multiply eq1 by 5

we get 20 u + 35 v = 10 ......eq3

Subtract eq2 and eq3

20 u+ 28 v - 20 u - 35 v = 9 -10

-7 v = -1

v = 1/7 .....eq4

put value of v into eq1

4u+7(1/7) = 2

4 u +1 = 2

4 u = 2-1

4 u = 1

u = 1/4 .....eq5

Put the value of u and v into 1/(x+1) = u and 1/(y+2) = v

1/(x+1) = u

1/(x+1) = 1/4

On cross multiplying ,we get x+1 = 4

x = 4-1

x = 3

1/(y+2) = v

1/(y+2) = 1/7

y+2 = 7

y = 7-2

y= 5

Hope it helps you.