The solutions of pair of equations is10x+y+ 2x-y=415x+y- 5x-y=-2

10x+y+ 2x-y=4 …(i)15x+y- 5x-y=-2 …(ii)Put 1x+y=a and 1x-y=bThe equations will become:10a + 2b = 4 …(1)15a – 5b = -2 …(2)Multiply equation (1) with 5 and (2) with 2, we get50a + 10b = 2030a – 10b = -4Adding both the equations80a = 16a = 15 Thus, 2 + 2b = 42b = 2b = 1Therefore, 1x+y=15 and 1x-y=1x + y = 5 and x – y = 1Now, on adding above two equations, we get2x = 6 x = 3which implies, 3 + y = 5y = 2Hence, the values are x = 3 and y = 2.

The solutions of pair of equations is10x+y+ 2x-y=415x+y- 5x-y=-2

10x+y+ 2x-y=4 …(i)15x+y- 5x-y=-2 …(ii)Put 1x+y=a and 1x-y=bThe equations will become:10a + 2b = 4 …(1)15a – 5b = -2 …(2)Multiply equation (1) with 5 and (2) with 2, we get50a + 10b = 2030a – 10b = -4Adding both the equations80a = 16a = 15 Thus, 2 + 2b = 42b = 2b = 1Therefore, 1x+y=15 and 1x-y=1x + y = 5 and x – y = 1Now, on adding above two equations, we get2x = 6 x = 3which implies, 3 + y = 5y = 2Hence, the values are x = 3 and y = 2.

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The solutions of pair of equations is

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

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

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x = 3 and y = 2

x = -3 and y = 2

x = 3 and y = -2

x = -3 and y = -2

answer is A.

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Detailed Solution

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

…(i)

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

…(ii)
Put

\frac{1}{x + y} = a

and

\frac{1}{x - y} = b

The equations will become:
10a + 2b = 4 …(1)
15a – 5b = -2 …(2)
Multiply equation (1) with 5 and (2) with 2, we get
50a + 10b = 20
30a – 10b = -4
Adding both the equations
80a = 16
a =