Solve for \(t\) in \(13t-14=3t+16\).
Solve for \(t\).
\[13t-14=3t+16\]
Add \(14\) to both sides.
\[13t=3t+16+14\]
Simplify \(3t+16+14\) to \(3t+30\).
\[13t=3t+30\]
Subtract \(3t\) from both sides.
\[13t-3t=30\]
Simplify \(13t-3t\) to \(10t\).
\[10t=30\]
Divide both sides by \(10\).
\[t=\frac{30}{10}\]
Simplify \(\frac{30}{10}\) to \(3\).
\[t=3\]
\[t=3\]
Substitute \(t=3\) into \(3(t-1)-2(2t+3)=5(t+3)\).
Start with the original equation.
\[3(t-1)-2(2t+3)=5(t+3)\]
Let \(t=3\).
\[3\times (3-1)-2\times (2\times 3+3)=5\times (3+3)\]
Simplify.
\[-12=30\]
\[-12=30\]
Since \(-12=30\) is not true, this is an inconsistent system.
