2. Solve the simultaneous equations \( 3 x+4 y=23 \) \( 2 x-4 y=2 \)

Solve the system of equations \( 3x+4y=23;2x-4y=2 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}3x+4y=23\\2x-4y=2\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}x=\frac{23-4y}{3}\\2x-4y=2\end{array}\right.\) - step2: Substitute the value of \(x:\) \(2\times \frac{23-4y}{3}-4y=2\) - step3: Simplify: \(\frac{2\left(23-4y\right)}{3}-4y=2\) - step4: Multiply both sides of the equation by LCD: \(\left(\frac{2\left(23-4y\right)}{3}-4y\right)\times 3=2\times 3\) - step5: Simplify the equation: \(46-20y=6\) - step6: Move the constant to the right side: \(-20y=6-46\) - step7: Subtract the numbers: \(-20y=-40\) - step8: Change the signs: \(20y=40\) - step9: Divide both sides: \(\frac{20y}{20}=\frac{40}{20}\) - step10: Divide the numbers: \(y=2\) - step11: Substitute the value of \(y:\) \(x=\frac{23-4\times 2}{3}\) - step12: Calculate: \(x=5\) - step13: Calculate: \(\left\{ \begin{array}{l}x=5\\y=2\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=5\\y=2\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(5,2\right)\) The solution to the simultaneous equations \(3x+4y=23\) and \(2x-4y=2\) is \(x=5\) and \(y=2\).