\( \begin{array}{l}2 y=x+3 \\ 5 y=x-7 \\ \text { What is the solution set of the given system? } \\ \{(-29 / 3,-10 / 3)\} \\ \{(1 / 3,4 / 3)\} \\ {[(-1 / 3,-4 / 3)\}} \\ {[(29 / 3,10 / 3)\}}\end{array} \)

Solve the system of equations \( 2y=x+3;5y=x-7 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2y=x+3\\5y=x-7\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=2y-3\\5y=x-7\end{array}\right.\) - step2: Substitute the value of \(x:\) \(5y=2y-3-7\) - step3: Simplify: \(5y=2y-10\) - step4: Move the variable to the left side: \(5y-2y=-10\) - step5: Subtract the terms: \(3y=-10\) - step6: Divide both sides: \(\frac{3y}{3}=\frac{-10}{3}\) - step7: Divide the numbers: \(y=-\frac{10}{3}\) - step8: Substitute the value of \(y:\) \(x=2\left(-\frac{10}{3}\right)-3\) - step9: Calculate: \(x=-\frac{29}{3}\) - step10: Calculate: \(\left\{ \begin{array}{l}x=-\frac{29}{3}\\y=-\frac{10}{3}\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=-\frac{29}{3}\\y=-\frac{10}{3}\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(-\frac{29}{3},-\frac{10}{3}\right)\) The solution set of the given system of equations is \( \{(x,y) = (-\frac{29}{3},-\frac{10}{3})\} \).