2. Lessow is /scssion 2 What is the solution of each system of equations? Show your work. a. \( 6 x-5 y=6 \) \( 4 x+y=3 \)

Solve the system of equations \( 6x-5y=6;4x+y=3 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}6x-5y=6\\4x+y=3\end{array}\right.\) - step1: Solve the equation: \(\left\{ \begin{array}{l}6x-5y=6\\y=3-4x\end{array}\right.\) - step2: Substitute the value of \(y:\) \(6x-5\left(3-4x\right)=6\) - step3: Simplify: \(26x-15=6\) - step4: Move the constant to the right side: \(26x=6+15\) - step5: Add the numbers: \(26x=21\) - step6: Divide both sides: \(\frac{26x}{26}=\frac{21}{26}\) - step7: Divide the numbers: \(x=\frac{21}{26}\) - step8: Substitute the value of \(x:\) \(y=3-4\times \frac{21}{26}\) - step9: Simplify: \(y=-\frac{3}{13}\) - step10: Calculate: \(\left\{ \begin{array}{l}x=\frac{21}{26}\\y=-\frac{3}{13}\end{array}\right.\) - step11: Check the solution: \(\left\{ \begin{array}{l}x=\frac{21}{26}\\y=-\frac{3}{13}\end{array}\right.\) - step12: Rewrite: \(\left(x,y\right) = \left(\frac{21}{26},-\frac{3}{13}\right)\) The solution to the system of equations \(6x-5y=6\) and \(4x+y=3\) is \(x=\frac{21}{26}\) and \(y=-\frac{3}{13}\).