Question

Solve the following system of equations
$2x+3y=9$
$3x+4y=5$

Answer 1

The given equations are
$2x+3y=9$ .........(i)
and $3x+4y=5$ ......(ii)
Multiplying equation (i) by $3$ and (ii) by $2$

$6x+9y=27$

$6x+8y=10$

and then subtracting, we get
$y=17$
Putting the value of $y=17$ in equation (i), we get
$2x+3\times 17=9$
$\Rightarrow 2x+51=9$
$\Rightarrow 2x=9-15$
$\Rightarrow 2x=-42$
$\Rightarrow x=-21$
Hence the required solution is $x=-21$ and $y=17.$