71. Solve the system of equations

$$
\left\{\begin{array}{l}
5 x+3 y=12 \\
2 x-y=7
\end{array}\right.
$$
Solution. Let's calculate the determinant of the system $\Delta$ and the determinants $\Delta_{x}$ and $\Delta_{y}:$

$$
\Delta=\left|\begin{array}{rr}
5 & 3 \\
2 & -1
\end{array}\right|=-11, \Delta_{x}=\left|\begin{array}{rr}
2 & 3 \\
7 & -1
\end{array}\right|=-33 ; \Delta_{y}=\left|\begin{array}{rr}
5 & 12 \\
2 & 7
\end{array}\right|=11
$$

We will find the values of $x$ and $y$ using Cramer's formulas:

$$
x=\frac{\Delta_{x}}{\Delta}=\frac{-33}{-11}=3 ; y=\frac{\Delta_{y}}{\Delta}=\frac{11}{-11}=-1
$$

Thus, the solution to the system is $(3, -1)$.