Remove parentheses.
\[\frac{x}{3}+1,y-\frac{2}{3}=\frac{5}{3},\frac{1}{3}\]
Subtract \(1,y\) from both sides.
\[\frac{x}{3}-\frac{2}{3}=\frac{5}{3}-1,y,\frac{1}{3}-1,y\]
Join the denominators.
\[\frac{x-2}{3}=\frac{5}{3}-1,y,\frac{1}{3}-1,y\]
Simplify \(\frac{5}{3}-1\) to \(\frac{2}{3}\).
\[\frac{x-2}{3}=\frac{2}{3},y,\frac{1}{3}-1,y\]
Simplify \(\frac{1}{3}-1\) to \(-\frac{2}{3}\).
\[\frac{x-2}{3}=y,y,\pm \frac{2}{3}\]
Break down the problem into these 4 equations.
\[\frac{x-2}{3}=\frac{2}{3}\]
\[\frac{x-2}{3}=y\]
\[\frac{x-2}{3}=-\frac{2}{3}\]
\[\frac{x-2}{3}=y\]
Solve the 1st equation: \(\frac{x-2}{3}=\frac{2}{3}\).
Multiply both sides by \(3\).
\[x-2=\frac{2}{3}\times 3\]
Cancel \(3\).
\[x-2=2\]
Add \(2\) to both sides.
\[x=2+2\]
Simplify \(2+2\) to \(4\).
\[x=4\]
\[x=4\]
Solve the 2nd equation: \(\frac{x-2}{3}=y\).
Multiply both sides by \(3\).
\[x-2=y\times 3\]
Regroup terms.
\[x-2=3y\]
Add \(2\) to both sides.
\[x=3y+2\]
\[x=3y+2\]
Solve the 3rd equation: \(\frac{x-2}{3}=-\frac{2}{3}\).
Multiply both sides by \(3\).
\[x-2=-\frac{2}{3}\times 3\]
Cancel \(3\).
\[x-2=-2\]
Cancel \(-2\) on both sides.
\[x=0\]
\[x=0\]
Solve the 4th equation: \(\frac{x-2}{3}=y\).
Multiply both sides by \(3\).
\[x-2=y\times 3\]
Regroup terms.
\[x-2=3y\]
Add \(2\) to both sides.
\[x=3y+2\]
\[x=3y+2\]
Collect all solutions.
\[x=4,3y+2,0\]
x=4,3*y+2,0
