Solve the following simultaneous equations. 2/x - 3/y = 15; 8/x + 5/y = 77

Question

Solve the following simultaneous equations.

 \(\frac{2}{x}-\frac{3}{y} = 15; \frac{8}{x}+\frac{5}{y} = 77\)

2/x - 3/y = 15; 8/x + 5/y = 77

Answer 1

The given simultaneous equations are

∴ Equations (i) and (ii) become

2p – 3q = 15 …(iii) 

8p + 5q = 77 …(iv)

Multiplying equation (iii) by 4, we get 

8p – 12q = 60 …(v) 

Subtracting equation (v) from (iv), we get

Substituting q = 1 in equation (iii), we get

Resubstituting the values of p and q, we get

\(\therefore\) (x, y) = \((\frac{1}{9}, 1)\) is the solution of the given simultaneous equations.