Question

If 2x + 3y = 12 and 3x − 2y = 5 then
(a) x = 2, y = 3 (b) x = 2, y = − 3 (c) x = 3, y = 2 (d) x = 3, y = − 2

Answer 1

The given system of equations is
$$\begin{gathered} 2x+3y=12.....\left(i\right) \\ 3x-2y=5.....\left(ii\right) \end{gathered}$$
Multiplying (i) by 2 and (ii) by 3 and then adding, we get
$$\begin{gathered} 4x+9x=24+15 \\ \Rightarrow x=\frac{39}{13}=3 \end{gathered}$$
Now, putting x = 3 in (i), we have
$2\times 3+3y=12\Rightarrow y=\frac{12-6}{3}=2$
Thus, x = 3 and y = 2.
Hence, the correct answer is option (c).