$\left\{\begin{array} { l } 4a+b=18 \\ -a-b=-6\end{array} \right.$
Sum the equations vertically to eliminate at least one variable$3a=12$
Divide both sides of the equation by $3$$a=4$
Substitute the given value of $a$ into the equation $a+b=6$$4+b=6$
Solve the equation for $b$$b=2$
The possible solution of the system is the ordered pair $\left( a, b\right)$$\left( a, b\right)=\left( 4, 2\right)$
Check if the given ordered pair is the solution of the system of equations$\left\{\begin{array} { l } 4 \times 4+2=18 \\ 4+2=6\end{array} \right.$
Simplify the equalities$\left\{\begin{array} { l } 18=18 \\ 6=6\end{array} \right.$
Since all of the equalities are true, the ordered pair is the solution of the system$\left( a, b\right)=\left( 4, 2\right)$