G7.1 2 apples and 3 oranges cost 6 dollars.
4 apples and 7 oranges cost 13 dollars.
16 apples and 23 oranges cost $C$ dollars. Find $C$.

G7.2 If $K=\frac{6 \cos \theta+5 \sin \theta}{2 \cos \theta+3 \sin \theta}$ and $\tan \theta=2$, find $K$.
Let the cost of one apple be $\$ x$ and one orange be $\$ y$.
$$
\begin{array}{l}
2 x+3 y=6 \ldots \ldots .(1) \\
4 x+7 y=13 \ldots \ldots .(2) \\
\text { (2) }-2(1): y=1, x=1.5 \\
C=16 x+23 y=24+23=47 \\
K=\frac{6 \frac{\cos \theta}{\cos \theta}+5 \frac{\sin \theta}{\cos \theta}}{2 \frac{\cos \theta}{\cos \theta}+3 \frac{\sin \theta}{\cos \theta}} \\
=\frac{6+5 \tan \theta}{2+3 \tan \theta} \\
=\frac{6+5 \times 2}{2+3 \times 2}=2
\end{array}
$$