Question

The number of solutions of simultaneous equations $4x+3y=6xy$; $8x+6y=9xy$ are ______

• A. $0$
• B. $2$
• C. $1$
• D. Infinite

Answer 1

The correct option is C $1$

Given two equations are

$4x+3y=6xy$ and ---- ( 1 )

$8x+6y=9xy$ ----- ( 2 )

Multiplying equation ( 1 ) with 2 we get,

$8x+6y=12xy$ ---- ( 3 )

Now comparing ( 2 ) and ( 3 ),we get

$\Rightarrow$ $12xy=9xy$

$\Rightarrow$ $xy=0$

If $x$ is $0$ substituting in any equation gives $y=0$

and vice versa.

$\therefore$ The only solution is $x=0$ and $y=0$

$\therefore$ Only one solution $(x,y)=(0,0)$