Solve the following pair of equations: 3x+2y=2xy and 6x+2y=3xy by Elimination Method
3x+2y=2xy —— (i)
6x+2y=3xy ——-(ii)
From equation (i) we get,
3x + 2y = 2xy
$\Rightarrow \frac{3x + 2y}{xy}$ = 2
$\Rightarrow \frac{3x}{xy} + \frac{2y}{xy}$ = 2
$\Rightarrow \frac{3}{y} + \frac{2}{x}$ = 2 —-(iii)
From equation (ii) we get,
6x+2y=3xy
$\Rightarrow \frac{6x + 2y}{xy}$ = 3
$\Rightarrow \frac{6x}{xy} + \frac{2y}{xy}$ = 3
$\Rightarrow \frac{6}{y} + \frac{2}{x}$ = 3 —-(iv)
Now Subtracting equations (iii) from (iv) we get,
($\frac{6}{y} + \frac{2}{x}$ )-($ \frac{3}{y} + \frac{2}{x}$) = 3-2
$\Rightarrow \frac{6}{y} – \frac{3}{y}$ = 1
$\Rightarrow \frac{6 – 3}{y}$ = 1
$\Rightarrow \frac{3}{y}$ = 1
$\Rightarrow y$ = 3
Substituting the value of y in equation (iv) we get,
$\frac{6}{y} + \frac{2}{x}$ = 3
$\Rightarrow \frac{6}{(3)} + \frac{2}{x}$ = 3
$\Rightarrow 2 + \frac{2}{x}$ = 3
$\Rightarrow \frac{2}{x}$ = 3 – 2
$\Rightarrow \frac{2}{x}$ = 1
$\Rightarrow x $= 2
∴ Required Solutions are x = 2 and y = 3.