Question

30/x-y +44/x+y =10 , 40/x-y +55/x+y =13. solve the equation ​

Answer 1

Given:-

→$\frac{30}{x-y}$+$\frac{44}{x+y}$=10๛(1)

→$\frac{40}{x-y}$+$\frac{55}{x+y}$=13๛(2)

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To Find:-

→The Values of x&y?

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AnsWer:-

★Using (1)★

→30($\frac{1}{x-y}$)+44($\frac{1}{x+y}$)=10

[๛Let $\frac{1}{x-y}$=u]

[๛Let $\frac{1}{x+y}$=v]

→30u+44v=10๛(3)

★Using (2)★

→40($\frac{1}{x-y}$)+55($\frac{1}{x+y}$)=13

[๛Let $\frac{1}{x-y}$=u]

[๛Let $\frac{1}{x+y}$=v]

→40u+55v=13๛(4)

♦Multiply eq-(3) with 4♦

•We get,

→120u+176v=40๛(5)

♦Multiply Eq-(4) with 3♦

→120u+165v=39๛(6)

ΠSubtract (5)&(6)Π

→120u+176v=40

→120u+165v=39

★Sign Changed★

→11v=1

→v=$\frac{1}{11}$๛(7)

★Use (7) in (3)★

→30u+$\cancel{44}$ × $\frac{1}{\cancel{11}}$=10

→30u+4=10

→30u=10-4

→30u=6

→u=$\frac{\cancel{6}}{\cancel{30}}$

→u=$\frac{1}{5}$๛(8)

♦But as $\frac{1}{x-y}$=u, and $\frac{1}{x+y}$=v♦

→$\frac{1}{x-y}$=$\frac{1}{5}$

★Cross Multiply★

→x-y=5๛(9)

•now,

→$\frac{1}{x+y}$=$\frac{1}{11}$

★Cross Multiply★

→x+y=11๛(10)

♦Add (9)&(10)♦

→x-y=5

→x+y=11

↑Signs Not-Changed↑

→2x=16

→x=$\frac{\cancel{16}}{\cancel{2}}$

→x=8๛(11)

♦Use (11) in (10)♦

→x+y=11

→8+y=11

→y=11-8

→y=3๛(12)

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♦From (11)&(12),We know♦

★x=8

★y=3

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Answer 2

QUESTION :

30/x-y +44/x+y =10 , 40/x-y +55/x+y =13. solve the equation

SOLUTION :

Suppose : 1 / X - Y = b

1 / X + Y = a.

NOW

The two equations become :

44 a + 30 b = 10......(1)

40b + 55 a = 13 .........(2)

Multiplying equation 1 by 4 and equation 2 by 3 we get :

176 a + 120 b = 40

120 b + 165 a = 39.

Subracting We get :

11 a = 1

a = 1/11

Similarly

b = 1 / 5

Now :

X + Y = 11

X - Y = 5

Hence :

X = 8.......(A1)

Y = 3......(A2)