Question

Solve the following pair of simultaneous equations:
$2x+3y=12;5x-3y=9$

• A. $x=1;y=0$
• B. $x=3;y=2$
• C. $x=7;y=3$
• D. $x=2;y=5$

Answer 1

The correct option is B $x=3;y=2$

Given equations are

$2x+3y=12\dots \left(i\right)$

$5x-3y=9\dots \left(ii\right)$

Add equations $\left(i\right)$ and $\left(ii\right)$ to eliminate $y$,

$\begin{array}{c}\underset{–}{\begin{array}{ccccc}2x& +& 3y& =& 12\\ 5x& -& 3y& =& 9\end{array}}\\ \begin{array}{ccccc}7x& & & =& 21\end{array}\\ x=3\end{array}$

Substitute this value in equation $\left(i\right)$,

$2\left(3\right)+3y=12$

$\Rightarrow 6+3y=12$

$\Rightarrow 3y=6$

$\Rightarrow y=2$

Therefore, the solution is $x=3,y=2$.