Determine which point from the specified set satisfies the system of equations. \( y=\frac{-1}{3} x+3 \) \( y=\frac{-3}{4} x+8 \) \( \begin{array}{l}\text { Select Choice } \\ \text { Select Choice } \\ (9,0) \\ (12,-1) \\ (-8,14)\end{array} \)

Solve the system of equations \( y=\frac{-1}{3}x+3;y=\frac{-3}{4}x+8 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}y=-\frac{1}{3}x+3\\y=-\frac{3}{4}x+8\end{array}\right.\) - step1: Substitute the value of \(y:\) \(-\frac{1}{3}x+3=-\frac{3}{4}x+8\) - step2: Multiply both sides of the equation by LCM: \(\left(-\frac{1}{3}x+3\right)\times 12=\left(-\frac{3}{4}x+8\right)\times 12\) - step3: Calculate: \(-4x+36=\left(-\frac{3}{4}x+8\right)\times 12\) - step4: Calculate: \(-4x+36=-9x+96\) - step5: Move the expression to the left side: \(-4x+9x=96-36\) - step6: Add and subtract: \(5x=96-36\) - step7: Add and subtract: \(5x=60\) - step8: Divide both sides: \(\frac{5x}{5}=\frac{60}{5}\) - step9: Divide the numbers: \(x=12\) - step10: Substitute the value of \(x:\) \(y=-\frac{1}{3}\times 12+3\) - step11: Simplify: \(y=-1\) - step12: Calculate: \(\left\{ \begin{array}{l}x=12\\y=-1\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=12\\y=-1\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(12,-1\right)\) The point that satisfies the system of equations is \( (12, -1) \).