Question

solve each of the following pairs of eqationsby reducing them to a pair of linear equation
10/x+y+2/x-y=4
15/x+y-5/x-y=-2​

Answer 1

Answer:

x = 3 and y = 2

Step-by-step explanation:

I believe your Question was,

"Solve each of the following pairs of eqations by reducing them to a pair of linear equation.

(10/(x + y)) + (2/(x - y) = 4

(15/(x + y) - (5/(x - y) = -2"

Let 1/(x + y) = p and 1/(x - y) = q

Thus,

10p + 2q = 4 ------ 1

15p - 5q = -2 ------ 2

Multiplying eq.1 with 5 and eq.2 with 2

50p + 10q = 20 ----- 3

30p - 10q = -4 ------ 4

Adding eq.3 and eq.4 we get,

50p + 10q = 20

+ 30p - 10q = -4

——————————

80p + 0 = 16

——————————

80p = 16

p = 16/80

p = 2/10

p = 1/5

Putting p = 1/5 in eq.1 we get,

10(1/5) + 2q = 4

2 + 2q = 4

2q = 4 - 2

2q = 2

q = 1

Now, we said that,

p = 1/(x + y)

1/5 = 1/(x + y)

x + y = 5 ------ 5

Also,

q = 1/(x - y)

1 = 1/(x - y)

x - y = 1 ------ 6

Adding eq.5 and eq.6

x + y = 5

+ x - y = 1

———————

2x + 0 = 6

———————

2x = 6

x = 6/2

x = 3

Putting x = 3 in eq.5 we get,

3 + y = 5

y = 5 - 3

y = 2

Thus, x = 3 and y = 2

Now, to be sure we can check this also,

(10/(x + y)) + (2/(x - y) = 4

(15/(x + y) - (5/(x - y) = -2

(10/(3 + 2)) + (2/(3 - 2)) = 4

10/5 + 2/1 = 4

2 + 2 = 4

4 = 4

Thus, it is correct for eq.1

(15/(3 + 2)) - (5/(3 - 2)) = -2

(15/5) - (5/1) = -2

3 - 5 = -2

-2 = -2

Thus, it is also correct for eq.2

Hope it helped and you understood it........All the best