Question

Content quality needed

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solve for x and y 25 /x+y - 3 /x-y =1 and 40 /x+y +2/x-y =5

Solve for x any y 15 /x + 2 /y =17 and 1 /x + 1/y = 36 / 15

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Answer 1

15/x+2/y=17..... eq (1)
1/x+1/y=36/15.....ek(2)
2×eq(2)
2/x+2/y=72/15...... eq (3)
eq (1)-(3)
15/x-2/x=17-72/15
13/x=255-72/15
1/x=183/15×13
x=195/183=1.06
put eq (1)
15/1.06+2/y=17
2/y=17-15/1.06
2/y=18.02-15/1.06
1/y=3.02/1.06×2
y=2.12/3.02
y=0.7
x=1.06andy=0.7
is your answer

Answer 2

Hi friend, Harish here.

Here is your answer:

1)

Given that:

$\frac{25}{(x+y)} - \frac{3}{(x-y)} = 1 \\ \\ \frac{40}{x+y} + \frac{2}{(x-y)} = 5$

Let: $\frac{1}{x+y} = a \& \frac{1}{x-y} = b$

Then,

⇒ 25a - 3b = 1    - (i)

⇒ 40a + 2b = 5   - (ii) 

Multiply (i) by 2  and (ii) by 3 and add :

⇒ $50a - 6b + 120a + 6b = 17$

⇒ $170a = 17$

⇒ $a = \frac{1}{10} = \frac{1}{x+y}$

So, x + y = 10 .

Now substituting the value of a in (ii):

$\frac{40}{10} + 2b = 5 \\ \\ 2b = 1 \\ \\ b = \frac{1}{2}$

So, x - y = 2.

And x + y = 10

Adding both we get:

2x = 12 

⇒ x = 6  and y = 4.
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2)  

Given that:

$\frac{15}{x}+ \frac{2}{y} = 17 \\ \\ \frac{1}{x}+ \frac{1}{y} = \frac{36}{15}$

Let:

$\frac{1}{x} = a \ \ \ \& \ \ \ \ \frac{1}{y} =b$

Then:

$15 a + 2 b = 17 \ \ \ \ \ \ \ \- (i) \\ \\ a+b = \frac{36}{5} \\ \\ 5a + 5b = 36 \ \ \ \ (ii)$

Now multiply (ii) by 3 and subtract (i) from (ii) 

⇒ $15a + 15b - 15a - 2b = 108 - 17 \\ \\ 13b = 91 \\ \\ b = \frac{91}{13} = 7$

Now, substituting value of b in (i) we get :

⇒ $15a + 2(7) = 17 \\ \\ 15 a = 3 \\ \\ a = \frac{1}{5}$

$\boxed{\bold{Therefore\ x = 5 \ \ \ and \ \ \ y = \frac{1}{7} }}$
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Hope my answer is helpful to you.