Solve the following simultaneous equations. 10/(x + y) + 2/(x - y) = 4; 15/(x + y) + 5/(x - y)

Question

Solve the following simultaneous equations.

\(\frac{10}{x+y} + \frac{2}{x-y} =4;\) \(\frac{15}{x+y} + \frac{5}{x-y} =-2\)

10/(x + y) + 2/(x - y) = 4; 15/(x + y) + 5/(x - y)

Answer 1

 The given simultaneous equations are

\(\therefore\) Equations (i) and (ii) become

10p + 2q = 4

\(\therefore\) 5p + q = 2 ....(iii)

[Dividing both sides by 2]

Substituting p = 1/5 in equation (iii), we get

Resubstituting the values of p and q, we get

Adding equations (vi) and (vii), we get

Substituting x = 3 in equation (vi), we get 

3 + y = 5 

∴ y = 5 – 3 = 2 

∴ (x, y) = (3, 2) is the solution of the given simultaneous equations.