Question

Consider a pair of equations as shown. 5/(x+2) + 7/(y+2)= 31/12 & 4/(x+2) + 3/(y+2)= 17/12 What is the value of x and y? *​

Answer 1

Answer:

Let 1/x-2 be u and 1/y+2 be v

5/(x+2) + 7/(y+2)=31/12

=> 5u + 7v = 31/12.............(1)

4/(x+2) + 3/(y+2) = 17/12

=> 4u + 3v = 17/12...............(2)

thus,

Multiplying 4 with equation (1) and 5 with equation (2)

We get,

4(5u+7v) = 4 × 31/12

=> 20u + 28v = 31/3........(3)

5(4u+3v) = 5× 17/12

=> 20u+15v = 85/12..........(4)

Subtacting (4) from (3)

20u + 28v - 20u - 15v = 31/3 - 85/12

=> 13v= 124-85/12

=>13v= 39/12

=> v = 39/12×13

=> v = 1/4

Therefore,

From equation (1),

5u+7v=31/12

=>5u +7×1/4 =31/12 [Substituting the value of v]

=>5u= 31/12-7/4

=>5u=5/6

=>u= 1/6

Therefore,

1/(x+2)=u

=> 1/(x+2)= 1/6 [Substituting the value of u]

=> x+2=6

=> x= 4

1/(y+2)= v

=> 1/(y+2)= 1/4 [Substituting the value of v]

=> y+2=4

=> y= 2

Answer 2

Answer:

x=4,y=2

Here's your answer.