Calculate: {\text{begin}array l 3x+y=10 } 2x-5y=1\text{end}array .

Expression: $\left\{\begin{array} { l } 3x+y=10 \\ 2x-5y=1\end{array} \right.$

Solve the equation for $y$

$\left\{\begin{array} { l } y=10-3x \\ 2x-5y=1\end{array} \right.$

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

$\left( x, y\right)=\left( 3, 1\right)$