$\left\{\begin{array} { l } 6x+10y=14 \\ 2x+3y=5\end{array} \right.$
Multiply both sides of the equation by $-3$$\left\{\begin{array} { l } 6x+10y=14 \\ -6x-9y=-15\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$y=-1$
Substitute the given value of $y$ into the equation $2x+3y=5$$2x+3 \times \left( -1 \right)=5$
Solve the equation for $x$$x=4$
The possible solution of the system is the ordered pair $\left( x, y\right)$$\left( x, y\right)=\left( 4, -1\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 3 \times 4+5 \times \left( -1 \right)=7 \\ 2 \times 4+3 \times \left( -1 \right)=5\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 7=7 \\ 5=5\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( x, y\right)=\left( 4, -1\right)$