Evaluate: {\text{begin}array l 2x-y=6 } 3x+6y=34\text{end}array .

Expression: $\left\{\begin{array} { l } 2x-y=6 \\ 3x+6y=34\end{array} \right.$

Multiply both sides of the equation by $6$

$\left\{\begin{array} { l } 12x-6y=36 \\ 3x+6y=34\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$15x=70$

Divide both sides of the equation by $15$

$x=\frac{ 14 }{ 3 }$

Substitute the given value of $x$ into the equation $2x-y=6$

$2 \times \frac{ 14 }{ 3 }-y=6$

Solve the equation for $y$

$y=\frac{ 10 }{ 3 }$

The possible solution of the system is the ordered pair $\left( x, y\right)$

$\left( x, y\right)=\left( \frac{ 14 }{ 3 }, \frac{ 10 }{ 3 }\right)$

Check if the given ordered pair is the solution of the system of equations

$\left\{\begin{array} { l } 2 \times \frac{ 14 }{ 3 }-\frac{ 10 }{ 3 }=6 \\ 3 \times \frac{ 14 }{ 3 }+6 \times \frac{ 10 }{ 3 }=34\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 6=6 \\ 34=34\end{array} \right.$

Since all of the equalities are true, the ordered pair is the solution of the system

$\left( x, y\right)=\left( \frac{ 14 }{ 3 }, \frac{ 10 }{ 3 }\right)$