1) \( -4 x+5 y=18 \) \( y=3 x-3 \)

Solve the system of equations \( -4x+5y=18;y=3x-3 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}-4x+5y=18\\y=3x-3\end{array}\right.\) - step1: Substitute the value of \(y:\) \(-4x+5\left(3x-3\right)=18\) - step2: Simplify: \(11x-15=18\) - step3: Move the constant to the right side: \(11x=18+15\) - step4: Add the numbers: \(11x=33\) - step5: Divide both sides: \(\frac{11x}{11}=\frac{33}{11}\) - step6: Divide the numbers: \(x=3\) - step7: Substitute the value of \(x:\) \(y=3\times 3-3\) - step8: Calculate: \(y=6\) - step9: Calculate: \(\left\{ \begin{array}{l}x=3\\y=6\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=3\\y=6\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(3,6\right)\) The solution to the system of equations is \( x = 3 \) and \( y = 6 \).