Question

7/(2x+1)+13/(y+2)=27;13/(2x+1)+7/(y+2)=33

Answer 1

Hi ,

7/(2x+1) + 13/(y+2) = 27---( 1 )

13/(2x+1) +7/(y+2) = 33---( 2 )

Let 1/(2x+1) = a ,

1/(y+2) = b ,

7a +13b = 27 ---( 3 )

13a + 7b = 33 ---( 4 )

Multiply equation ( 1 ) with 13 , and

equation ( 2 ) with 7 , we get

91a + 169b = 351 ---( 5 )

91a + 49b = 231 ---( 6 )

Subtract equation ( 6 ) from equation

( 5 ) , we get

120b = 120

b = 120/120

b = 1

Put b = 1 in equation ( 3 ) we get ,

7a + 13 = 27

7a = 27 - 13

7a = 14

a = 14/7

a = 2

Now ,

a = 2 and b = 1

1/( 2x + 1 ) = 2 ; 1/( y + 2 ) = 1

2x + 1 = 1/2 ; y + 2 = 1

2x = 1/2 - 1 ; y = 1 - 2

2x = -1/2 ; y = -1

x = - 1/4 ; y = -1

Therefore ,

x = -1/4 ; y = -1

I hope this helps you.

: )

Answer 2

Hello Dear.

Here is your answer---


Let 1/(2x +1) be a and 1/(y + 2) = b

Thus, 7a + 13b = 27  ---------------------------eq(i)
     
    & 13a + 7b = 33  ----------------------------eq(ii)

From eq(i),

 7a = 27 - 13b
  a = (27 - 13b)/7

Putting the Value of a in eq(i),

              13a + 7b = 33
⇒ 13[(27 -13b)/7] + 7b = 33

⇒  $\frac{351 - 169b + 49}{7}$ = 33

⇒ 400 -169b = 33 × 7

⇒ 400 - 169b = 231

⇒ 169b = 400 - 231

⇒ 169b = 169

Thus, b = 1

Putting b = 1 in eq(i),

  7a + 13b = 27
  7a + 13(1) = 27
  7a = 27 - 13
  7a = 14
   a = 2

For x and y,

1/(2x + 1) = a
 1 = 2 × (2x + 1)
 4x + 2 = 1
  4x = -1
  x = -1/4

Also, 1/(y + 2) = b
 1 = 1 × (y+ 2)
 y + 2 = 1
 y = -2 + 1
 y = -1

Thus, values of x and y are -1/4 and -1 respectively.


Hope it helps.


Have a nice day.