Solve the system by graphing \( \begin{array}{l}y=\frac{1}{2} x-2 \\ y=4 x+5\end{array} \)

Solve the system of equations \( y=\frac{1}{2}x-2;y=4x+5 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}y=\frac{1}{2}x-2\\y=4x+5\end{array}\right.\) - step1: Substitute the value of \(y:\) \(\frac{1}{2}x-2=4x+5\) - step2: Multiply both sides of the equation by LCM: \(\left(\frac{1}{2}x-2\right)\times 2=\left(4x+5\right)\times 2\) - step3: Calculate: \(x-4=\left(4x+5\right)\times 2\) - step4: Calculate: \(x-4=8x+10\) - step5: Move the expression to the left side: \(x-8x=10+4\) - step6: Add and subtract: \(-7x=10+4\) - step7: Add and subtract: \(-7x=14\) - step8: Change the signs: \(7x=-14\) - step9: Divide both sides: \(\frac{7x}{7}=\frac{-14}{7}\) - step10: Divide the numbers: \(x=-2\) - step11: Substitute the value of \(x:\) \(y=\frac{1}{2}\left(-2\right)-2\) - step12: Simplify: \(y=-3\) - step13: Calculate: \(\left\{ \begin{array}{l}x=-2\\y=-3\end{array}\right.\) - step14: Check the solution: \(\left\{ \begin{array}{l}x=-2\\y=-3\end{array}\right.\) - step15: Rewrite: \(\left(x,y\right) = \left(-2,-3\right)\) The solution to the system of equations \(y=\frac{1}{2}x-2\) and \(y=4x+5\) is \(x=-2\) and \(y=-3\).