8. Solve for x and y:\begin{array}{l}{\frac{57}{x+y}+\frac{6}{x-y}=5}

1.	8. Solve for x and y:\begin{array}{l}{\frac{57}{x+y}+\frac{6}{x-y}=5} \\ {\frac{38}{x+y}+\frac{21}{x-y}=9, x+y \neq 0, x-y \neq 0}\end{array}
Answer» [57/x+y]+[6/x-y]=5 ......(1) [57(1/x+y)]+[6(1/x-y)]=5 [38/x+y]+[21/x-y]=9 ......(2) [38(1/x+y)]+[21(1/x-y)]=9 Let 1/x+y = A & 1/x-y = B therefore, 57A+6B=5 .......(3) 38A=21B=9 .......(4) Now, (3)7 & (4)2 = 399A+42B=35 76A+42B=18 (-) (-) (-) ___________ 323A = 17 A=17/323 A=1/19 .....(5) put (5)in (4)= 38*(1/19)+21B=9 2+21B=9 21B=9-2 21B=7 B=7/21 B=1/3 ....(6) 1/x+y = A & 1/x-y = B= x+y=1/A=19 x+y=19 ....(7) x-y=1/B=3 x-y=3 ....(8) Add (7)+(8)= x+y=19 x -y= 3 ______ 2x = 22 x=11 & y=8

8. Solve for x and y:\begin{array}{l}{\frac{57}{x+y}+\frac{6}{x-y}=5} \\ {\frac{38}{x+y}+\frac{21}{x-y}=9, x+y \neq 0, x-y \neq 0}\end{array}

Answer»

[57/x+y]+[6/x-y]=5 ......(1)

[57*(1/x+y)]+[6*(1/x-y)]=5

[38/x+y]+[21/x-y]=9 ......(2)

[38*(1/x+y)]+[21*(1/x-y)]=9

Let 1/x+y = A & 1/x-y = B

therefore,

57A+6B=5 .......(3)

38A=21B=9 .......(4)

Now,

(3)*7 & (4)*2

399A+42B=35

76A+42B=18

(-) (-) (-)

___________

323A = 17

A=17/323

A=1/19 .....(5)

put (5)in (4)=

38*(1/19)+21B=9

2+21B=9

21B=9-2

21B=7

B=7/21

B=1/3 ....(6)

1/x+y = A & 1/x-y = B=

x+y=1/A=19

x+y=19 ....(7)

x-y=1/B=3

x-y=3 ....(8)

Add (7)+(8)=

x+y=19

x -y= 3

______

2x = 22

x=11 &

y=8