13. \( \begin{aligned}-1 x-16 y & =-1 \\ 33 x+16 y & =19\end{aligned} \)

Solve the system of equations \( -x-16y=-1;33x+16y=19 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-x-16y=-1\\33x+16y=19\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=1-16y\\33x+16y=19\end{array}\right.\) - step2: Substitute the value of \(x:\) \(33\left(1-16y\right)+16y=19\) - step3: Simplify: \(33-512y=19\) - step4: Move the constant to the right side: \(-512y=19-33\) - step5: Subtract the numbers: \(-512y=-14\) - step6: Change the signs: \(512y=14\) - step7: Divide both sides: \(\frac{512y}{512}=\frac{14}{512}\) - step8: Divide the numbers: \(y=\frac{7}{256}\) - step9: Substitute the value of \(y:\) \(x=1-16\times \frac{7}{256}\) - step10: Calculate: \(x=\frac{9}{16}\) - step11: Calculate: \(\left\{ \begin{array}{l}x=\frac{9}{16}\\y=\frac{7}{256}\end{array}\right.\) - step12: Check the solution: \(\left\{ \begin{array}{l}x=\frac{9}{16}\\y=\frac{7}{256}\end{array}\right.\) - step13: Rewrite: \(\left(x,y\right) = \left(\frac{9}{16},\frac{7}{256}\right)\) The solution to the system of equations is \( (x,y) = \left(\frac{9}{16},\frac{7}{256}\right) \) or \( (x,y) = (0.5625,0.02734375) \).