Given the system of equations, what is the solution? \( \begin{array}{l}3 x-2 y+10=0 \\ 5 y=4 x+8 \\ \{(-34 / 7,-16 / 7)\} \\ \{(-34 / 7,16 / 7)\} \\ \{(34 / 7,-16 / 7)\}\end{array} \)

Solve the system of equations \( 3x-2y+10=0;5y=4x+8 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x-2y+10=0\\5y=4x+8\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{2y-10}{3}\\5y=4x+8\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5y=4\times \frac{2y-10}{3}+8\) - step3: Simplify: \(5y=\frac{4\left(2y-10\right)}{3}+8\) - step4: Multiply both sides of the equation by LCD: \(5y\times 3=\left(\frac{4\left(2y-10\right)}{3}+8\right)\times 3\) - step5: Simplify the equation: \(15y=8y-16\) - step6: Move the variable to the left side: \(15y-8y=-16\) - step7: Subtract the terms: \(7y=-16\) - step8: Divide both sides: \(\frac{7y}{7}=\frac{-16}{7}\) - step9: Divide the numbers: \(y=-\frac{16}{7}\) - step10: Substitute the value of \(y:\) \(x=\frac{2\left(-\frac{16}{7}\right)-10}{3}\) - step11: Calculate: \(x=-\frac{34}{7}\) - step12: Calculate: \(\left\{ \begin{array}{l}x=-\frac{34}{7}\\y=-\frac{16}{7}\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=-\frac{34}{7}\\y=-\frac{16}{7}\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(-\frac{34}{7},-\frac{16}{7}\right)\) The solution to the system of equations is \( (x,y) = (-\frac{34}{7},-\frac{16}{7}) \) or \( (x,y) = (-4.857142, -2.285714) \).