Solve for \(x\) in \(5x-8y=1\).
Solve for \(x\).
\[5x-8y=1\]
Add \(8y\) to both sides.
\[5x=1+8y\]
Divide both sides by \(5\).
\[x=\frac{1+8y}{5}\]
\[x=\frac{1+8y}{5}\]
Substitute \(x=\frac{1+8y}{5}\) into \(5x-12y=3\).
Start with the original equation.
\[5x-12y=3\]
Let \(x=\frac{1+8y}{5}\).
\[5\times \frac{1+8y}{5}-12y=3\]
Simplify.
\[1-4y=3\]
\[1-4y=3\]
Solve for \(y\) in \(1-4y=3\).
Solve for \(y\).
\[1-4y=3\]
Subtract \(1\) from both sides.
\[-4y=3-1\]
Simplify \(3-1\) to \(2\).
\[-4y=2\]
Divide both sides by \(-4\).
\[y=-\frac{2}{4}\]
Simplify \(\frac{2}{4}\) to \(\frac{1}{2}\).
\[y=-\frac{1}{2}\]
\[y=-\frac{1}{2}\]
Substitute \(y=-\frac{1}{2}\) into \(x=\frac{1+8y}{5}\).
Start with the original equation.
\[x=\frac{1+8y}{5}\]
Let \(y=-\frac{1}{2}\).
\[x=\frac{1+8\times \frac{-1}{2}}{5}\]
Simplify.
\[x=-\frac{3}{5}\]
\[x=-\frac{3}{5}\]
Therefore,
\[\begin{aligned}&x=-\frac{3}{5}\\&y=-\frac{1}{2}\end{aligned}\]
x=-3/5;y=-1/2
