Question

Solve for x and y:
$$\begin{gathered} x-y=3 \\ \frac{x}{3}+\frac{y}{2}=6 \end{gathered}$$

Answer 1

The given system of equations is
$$\begin{gathered} x-y=3.....\left(i\right) \\ \frac{x}{3}+\frac{y}{2}=6.....\left(ii\right) \end{gathered}$$
From (i), write y in terms of x to get
$y=x-3$
Substituting y = x − 3 in (ii), we get
$$\begin{gathered} \frac{x}{3}+\frac{x-3}{2}=6 \\ \Rightarrow 2x+3\left(x-3\right)=36 \\ \Rightarrow 2x+3x-9=36 \\ \Rightarrow x=\frac{45}{5}=9 \end{gathered}$$
Now, substituting x = 9 in (i), we have
$$\begin{gathered} 9-y=3 \\ \Rightarrow y=9-3=6 \end{gathered}$$
Hence, x = 9 and y = 6.