$\left\{\begin{array} { l } y=10-3x \\ 2x-5y=1\end{array} \right.$
Substitute the given value of $y$ into the equation $2x-5y=1$$2x-5\left( 10-3x \right)=1$
Solve the equation for $x$$x=3$
Substitute the given value of $x$ into the equation $y=10-3x$$y=10-3 \times 3$
Solve the equation for $y$$y=1$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 3, 1\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 3 \times 3+1=10 \\ 2 \times 3-5 \times 1=1\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 10=10 \\ 1=1\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 3, 1\right)$