Question

3/x+y + 2/x-y = 3
2/x+y + 3/x-y = 11/3​

Answer 1

Answer:

Step-by-step explanation:

$\frac{3}{x+y} +\frac{2}{x-y} = 3$ - eq(i)

        &

$\frac{2}{x+y} +\frac{3}{x-y} = \frac{11}{3}$ - eq(ii)

Let, $\frac{1}{x+y}$=u and $\frac{1}{x-y}$=v

∴ $3u+2v=3$ - eq(iii)

             &

$2u+3v=\frac{11}{3}$ - eq(iv)

after multiplying eq(iii) to 2 and eq(iv) to 3, we get:

6u+4v=6 - eq(v)

     &

6u+9v=11 - eq(vi)

After substracting eq(v) from eq(vi), we get:

0+(9-4)v=11-6

∴ 5v=5

∴ v = 1

After substituting the value of v in eq(iii), we get:

3u+2(1)=3

∴3u=3-2=1

∴u=$\frac{1}{3}$

$\frac{1}{x+y}=u$

∴$\frac{1}{x+y}= \frac{1}{3}$

∴x+y=3 - eq (vii)

∵ We let the value of $\frac{1}{x-y}$ be v

∴$\frac{1}{x-y}$=1

∴x-y=1 - eq(viii)

After adding eq(vii) and eq(viii), we get:

x+y+x-y=1+3

∴2x=4

∴x=2

After substituting the value of x in eq(vii), We get:

2+y=3

∴y=3-2=1

And hence x=2 and y=1