Solve for \(y\) in \(y=-4y+14.\).
Solve for \(y\).
\[y=-4y+14.\]
Add \(4y\) to both sides.
\[y+4y=14.\]
Simplify \(y+4y\) to \(5y\).
\[5y=14.\]
Divide both sides by \(5\).
\[y=\frac{14.}{5}\]
\[y=\frac{14.}{5}\]
Substitute \(y=\frac{14.}{5}\) into \(x-2y=9\).
Start with the original equation.
\[x-2y=9\]
Let \(y=\frac{14.}{5}\).
\[x-2\times \frac{14.}{5}=9\]
Simplify.
\[x-\frac{2\times 14.}{5}=9\]
\[x-\frac{2\times 14.}{5}=9\]
Substitute \(y=\frac{14.}{5}\) into \(2x-4y=18\).
Start with the original equation.
\[2x-4y=18\]
Let \(y=\frac{14.}{5}\).
\[2x-4\times \frac{14.}{5}=18\]
Simplify.
\[2x-\frac{4\times 14.}{5}=18\]
\[2x-\frac{4\times 14.}{5}=18\]
Substitute \(y=\frac{14.}{5}\) into \(8x+2y=7\).
Start with the original equation.
\[8x+2y=7\]
Let \(y=\frac{14.}{5}\).
\[8x+2\times \frac{14.}{5}=7\]
Simplify.
\[8x+\frac{2\times 14.}{5}=7\]
\[8x+\frac{2\times 14.}{5}=7\]
Solve for \(x\) in \(x-\frac{2\times 14.}{5}=9\).
Solve for \(x\).
\[x-\frac{2\times 14.}{5}=9\]
Add \(\frac{2\times 14.}{5}\) to both sides.
\[x=9+\frac{2\times 14.}{5}\]
\[x=9+\frac{2\times 14.}{5}\]
Substitute \(x=9+\frac{2\times 14.}{5}\) into \(2x-\frac{4\times 14.}{5}=18\).
Start with the original equation.
\[2x-\frac{4\times 14.}{5}=18\]
Let \(x=9+\frac{2\times 14.}{5}\).
\[2(9+\frac{2\times 14.}{5})-\frac{4\times 14.}{5}=18\]
Simplify.
\[18+\frac{4\times 14.}{5}-\frac{4\times 14.}{5}=18\]
\[18+\frac{4\times 14.}{5}-\frac{4\times 14.}{5}=18\]
Since \(18+\frac{4\times 14.}{5}-\frac{4\times 14.}{5}=18\) is not true, this is an inconsistent system.
