# Solve for: {\text{begin}array l 4a+b=18 } a+b=6\text{end}array .

## Expression: $\left\{\begin{array} { l } 4a+b=18 \\ a+b=6\end{array} \right.$

Multiply both sides of the equation by $-1$

$\left\{\begin{array} { l } 4a+b=18 \\ -a-b=-6\end{array} \right.$

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

$\left( a, b\right)=\left( 4, 2\right)$

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