Question

Solve the following systems of linear equations by using the method of elimination by equating the coefficients:
(i) $3x+2y=11$
(ii)$2x+3y=4$

Answer 1

The given systems of equations is
$3x+2y=11$ $\left(i\right)$
$2x+3y=4$ $\left(ii\right)$

Let us eliminate $y$ from the given equations. The coefficients of $y$ in the given equations are $2$ and $3$ respectively. The L.C.M. of $2$ and $3$ is $6$. So, we make the coefficients of $y$ equal to $6$ in the two equations.

Multiplying $\left(i\right)$ by $3$ and $\left(ii\right)$ by $2$, we get
$9x+6y=33$ ...$\left(iii\right)$
$4x+6y=8$ ..$\left(iv\right)$

Subtracting $\left(iv\right)$ from $\left(iii\right)$, we get
$5x=25\Rightarrow x=5$

Substituting $x=5$ equation in $\left(i\right)$, we get
$15+2y=11\Rightarrow 2y=-4\Rightarrow y=-2$

Hence, the solution of the given system of equations is $x=5,y=-2$.