Question

solve the following set of linear equation in two variables : 10/(x+y) + 2/(x-y)=4, 15/(x+y)-5/(x-y)=-2. what is the value of x & y?​

Answer 1

Step-by-step explanation:

Given:

$\frac{10}{ x+ y} + \frac{2}{x - y} = 4 \\ \\ \frac{15}{x + y} - \frac{5}{x - y} = - 2$

To find: Find the value of x and y.

Solution:

Step 1: Convert given equations into standard linear equations in two another unknowns.

Let

$\frac{1}{x + y} = a \: ...eq1 \\ \\ \frac{1}{x - y} = b \: ...eq2$

put these values in the given eqs

$10a + 2b = 4 \: ...eq3 \\ 15a - 5b = - 2 \: ...eq4$

Step 2: Find the values of a and b

Take 2 common from eq3 and cancel from both sides.

$\cancel2(5a + b) = \cancel2 \times 2 \\ \\ 5a + b = 2 \: ...eq5$

Multiply eq5 by 5 and add with eq4

$25a + 5b = 10 \\ 15a - 5b = - 2 \\ - - - - - - - \\ 40a = 8 \\ \\ a = \frac{8}{40} \\ \\ a = \frac{1}{5}$

put value of a in eq5

$5 \times \frac{1}{5} + b = 2 \\ \\ 1 + b = 2 \\ \\ b = 2 - 1 \\ \\ b = 1$

Step 3: Put values of a and b in eq1 and eq2; to find value of x and y

$\frac{1}{x + y} = \frac{1}{5} \\ \\ or \\ \\ x + y = 5 \: ...eq6 \\ \\ \frac{1}{x - y} = 1 \\ \\ or \\ \\ x - y = 1 \: ...eq7$

add both eqs 6 and 7

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

put value of x in eq6

$3 + y = 5 \\ \\ y = 5 - 3 \\ \\ y = 2$

Final answer:

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

Hope it helps you.

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