Question

solve for x and y: 1/x+1 + 1/y+1 = 10; 1/x+1 - 1/y+1 = 4

Answer 1

using simultaneous equations 
   1/x +1+1/y+1=10 ....(1)
    1/x+1-1/y+1=4........(2)
adding both the equations

    1/x +1+1/y+1=10 
+  1/x+1-1/y+1=4
=   2/x+2+2=14
=   2/x+4=14
=   2/x=14-4
=   2/x=10
=   x=2/10 = 1/5 = 0.2

put x=0.2 in equation (1)
1/x +1+1/y+1=10 
1/0.2+1+1/y+1=10......(3)
5+1/y+2=10
5+1/y=10-2
5+1/y=8
5+1/y=8
1/y=8-5
1/y=3
1=3y
y=1/3 = 0.333333

ans. x=0.2
        y= 0.333333

Answer 2

Let the equations are

$\sf \frac{1}{x + 1} + \frac{1}{y + 1} = 10 \: \: \: \: \: \: \: \: \: \: \: ...(1) \\ \sf \frac{1}{x + 1} - \frac{1}{y + 1} = 4 \: \: \: \: \: \: \: \: \: \: \: ...(2)$

To Find the values of x and y

Then,

$\sf \frac{1}{x + 1} + \frac{1}{y + 1} + \frac{1}{x + 1} - \frac{1}{y + 1} =10+4$

$\sf \frac{2}{x + 1} =14$

$\sf \frac{1}{x + 1} =7$

$\purple {{{\sf x= \frac{-6}{7}}}}$

Now, Substrate eqn 1 and eqn 2

$\sf \frac{1}{x + 1} + \frac{1}{y + 1} - \frac{1}{x + 1} - \frac{1}{y + 1} =10-4$

$\sf \frac{2}{y+ 1} =6$

$\sf y+1 = \frac{1}{3}$

$\purple {{{\sf y = \frac{-2}{3}}}}$

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