Solve for \(y\) in \(3x+y-2z=2\).
Solve for \(y\).
\[3x+y-2z=2\]
Subtract \(3x\) from both sides.
\[y-2z=2-3x\]
Add \(2z\) to both sides.
\[y=2-3x+2z\]
\[y=2-3x+2z\]
Substitute \(y=2-3x+2z\) into \(-6x-2y+4z=-2\).
Start with the original equation.
\[-6x-2y+4z=-2\]
Let \(y=2-3x+2z\).
\[-6x-2(2-3x+2z)+4z=-2\]
Simplify.
\[-4=-2\]
\[-4=-2\]
Since \(-4=-2\) is not true, this is an inconsistent system.
