23 Solve the simultaneous equations. You must show all your working. \[ \begin{array}{r}3 x-2 y=19 \\ x+y=3\end{array} \]

Solve the system of equations \( 3x-2y=19;x+y=3 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x-2y=19\\x+y=3\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}3x-2y=19\\x=3-y\end{array}\right.\) - step2: Substitute the value of \(x:\) \(3\left(3-y\right)-2y=19\) - step3: Simplify: \(9-5y=19\) - step4: Move the constant to the right side: \(-5y=19-9\) - step5: Subtract the numbers: \(-5y=10\) - step6: Change the signs: \(5y=-10\) - step7: Divide both sides: \(\frac{5y}{5}=\frac{-10}{5}\) - step8: Divide the numbers: \(y=-2\) - step9: Substitute the value of \(y:\) \(x=3-\left(-2\right)\) - step10: Substitute back: \(x=3+2\) - step11: Calculate: \(x=5\) - step12: Calculate: \(\left\{ \begin{array}{l}x=5\\y=-2\end{array}\right.\) - step13: Check the solution: \(\left\{ \begin{array}{l}x=5\\y=-2\end{array}\right.\) - step14: Rewrite: \(\left(x,y\right) = \left(5,-2\right)\) The solution to the simultaneous equations is \( x = 5 \) and \( y = -2 \).