Question

10/x+y +2/x-y=4
15/x+y - 5/x-y=-2

Answer 1

Step-by-step explanation:

let 1/x+y = p

let 1/x-y = q

substituting,

10p + 2q = 4 --1

15p + 5q = -2 --2

solving linear equation, by eliminating,

5(10p + 2q = 4) = 50p + 10q = 20

2(15p + 5q = -2) = 30p + 10q = -4

Subtracting,

50p + 10q = 20

(-) (-)30p + (-)10q = (+)-4

______________________

20p = 24

p = 24/20 or 6/5.

10p + 2q = 4

10× 6/5 + 2q = 4

12 + 2q = 4

2q = 4-12

q = -8/2 = -4

p= 6/5 q= -4

1/x+y = 6/5

6x+6y=5 -------- 3

1/x-y = -4

-4x+4y=1 ----------4

by eliminating,

4(6x+6y=5) = 24x + 24y = 20

6(-4x+4y=1) = -24x+ 24y = 6

24x + 24y = 20

-24x + 24y = 6

_____________

48y=26

y = 26/48 = 13/24

OR

24x + 24y = 20

(+)-24x +(-)24y = (-)6

________________

48x = 14

x = 14/48 = 7/24

X = 7/24 Y = 13/24

hope it helps..

hard question

Solved

((((( HENCE PROVED )))))

@12/4/21

Answer 2

Step-by-step explanation:

Given:

$\frac{10}{x + y} + \frac{2}{x - y} = 4 \: \: \: ...eq1\\ \\ \frac{15}{x + y} - \frac{5}{x - y} = - 2 \: \: \: ...eq2$

To find : Solution of equation.

Solution:

Step 1: Convert given equations in linear equations in two variables.

let

$\frac{1}{x - y} = a \: \: \: ...eq3 \\ \\ \frac{1}{x + y} = b \: \: \: ...eq4$

$\bold{\red{10a + 2b = 4}} \: \: \: ...eq5 \\ \bold{\green{15a - 5b = - 2}} \: \: \: ...eq6$

Step 2: Solve eq5 and eq6 and find values of a and b.

Multiply eq5 by 5 and eq6 by 2 and add both equations

$50a + 10b = 20 \\ 30a - 10b = - 4 \\ - - - - - - - - \\ 80a = 16 \\ \\ a = \frac{16}{80} \\ \\ \bold{\purple{a = \frac{1}{5}}}$

put value of a in eq5

$10 \times \frac{1}{5} + 2b = 4 \\ \\ 2 + 2b = 4 \\ \\ 2b = 4 - 2 \\ \\ 2b = 2 \\ \\\bold{\pink{ b = 1}}$

Step 3: Put the value of a and b in eq3 and eq4

$\frac{1}{x + y} = \frac{1}{5} \\ \\ or \\ \\ \bold{\green{x + y = 5}} \: \: \: ...eq7 \\ \\ \frac{1}{x - y} = \frac{1}{1} \\ \\ or \\ \\\bold{\red{ x - y = 1}} \: \: \: ...eq8$

add eq7 and eq8

$x + y = 5 \\ x - y = 1 \\ - - - - - - - \\ 2x = 6 \\ \\ x = \frac{6}{2} \\ \\ \bold{\red{x = 3}}$

put value of x in eq7

$3 + y = 5 \\ \\ y = 5 - 3 \\ \\ \bold{\green{y = 2 }}$

Final answer:

Value of x and y are

$\bold{\red{x = 3}} \\ \\ \bold{\green{y = 2 }}$

Hope it helps you.

To learn more on brainly:

1) 22/x+y+15/x-y=5,55/x+y +40/x-y=13

https://brainly.in/question/42309773

2)find x and y for the following equations.

https://brainly.in/question/43906292