Solve for \(x\) in \(\frac{1}{2}(x+3)=0\).
Solve for \(x\).
\[\frac{1}{2}(x+3)=0\]
Simplify \(\frac{1}{2}(x+3)\) to \(\frac{x+3}{2}\).
\[\frac{x+3}{2}=0\]
Multiply both sides by \(2\).
\[x+3=0\times 2\]
Simplify \(0\times 2\) to \(0\).
\[x+3=0\]
Subtract \(3\) from both sides.
\[x=-3\]
\[x=-3\]
Substitute \(x=-3\) into \(\frac{1}{6}x-y=\frac{41}{2}\).
Start with the original equation.
\[\frac{1}{6}x-y=\frac{41}{2}\]
Let \(x=-3\).
\[\frac{1}{6}\times -3-y=\frac{41}{2}\]
Simplify.
\[-\frac{1}{2}-y=\frac{41}{2}\]
\[-\frac{1}{2}-y=\frac{41}{2}\]
Solve for \(y\) in \(-\frac{1}{2}-y=\frac{41}{2}\).
Solve for \(y\).
\[-\frac{1}{2}-y=\frac{41}{2}\]
Add \(\frac{1}{2}\) to both sides.
\[-y=\frac{41}{2}+\frac{1}{2}\]
Simplify \(\frac{41}{2}+\frac{1}{2}\) to \(21\).
\[-y=21\]
Multiply both sides by \(-1\).
\[y=-21\]
\[y=-21\]
Therefore,
\[\begin{aligned}&x=-3\\&y=-21\end{aligned}\]
x=-3;y=-21
