Question

Solve the following pairs of linear equations :
$2x+3y=2xy,6x+12y=7xy$

Answer 1

$2x+3y=2xy$ ............ (1)

$6x+12y=7xy$ ........... (2)

Multiply the equation (1) by $3$ and subtract the result from equation (2),

$6x+12y=7xy$ ........... (2)

$6x+9y=6xy$ ............ (3)

$6x+12y-6x-9y=7xy-6xy$

$3y=xy$

$3y-xy=0$

$y(3-x)=0$

$y=0$ or $x=3$

Substitute $y=0$ in equation (1),

$2x+0=0$

$x=0$

So, one solution is $x=0,y=0$

Substitute $x=3$ in equation (1),

$2\left(3\right)+3y=2\left(3\right)y$

$6+3y=6y$

$3y=6$

$y=2$

So, the second solution is $x=3,y=2$