Evaluate: {\text{begin}array l y=(1)/(4)x+1 } y=-x-9\text{end}array .

Expression: $\left\{\begin{array} { l } y=\frac{ 1 }{ 4 }x+1 \\ y=-x-9\end{array} \right.$

Simplify the expression

$\left\{\begin{array} { l } -x+4y=4 \\ y=-x-9\end{array} \right.$

Simplify the expression

$\left\{\begin{array} { l } -x+4y=4 \\ x+y=-9\end{array} \right.$

Sum the equations vertically to eliminate at least one variable

$5y=-5$

Divide both sides of the equation by $5$

$y=-1$

Substitute the given value of $y$ into the equation $-x+4y=4$

$-x+4 \times \left( -1 \right)=4$

Solve the equation for $x$

$x=-8$

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

$\left( x, y\right)=\left( -8, -1\right)$

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

$\left\{\begin{array} { l } -1=\frac{ 1 }{ 4 } \times \left( -8 \right)+1 \\ -1=-\left( -8 \right)-9\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } -1=-1 \\ -1=-1\end{array} \right.$

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

$\left( x, y\right)=\left( -8, -1\right)$