Graph the system below and write its solution. \[ \begin{array}{c}2 x+y=4 \\ y=-\frac{1}{2} x-2\end{array} \]

Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+y=4\\y=-\frac{1}{2}x-2\end{array}\right.\) - step1: Substitute the value of \(y:\) \(2x-\frac{1}{2}x-2=4\) - step2: Subtract the terms: \(\frac{3}{2}x-2=4\) - step3: Move the constant to the right side: \(\frac{3}{2}x=4+2\) - step4: Add the numbers: \(\frac{3}{2}x=6\) - step5: Multiply by the reciprocal: \(\frac{3}{2}x\times \frac{2}{3}=6\times \frac{2}{3}\) - step6: Multiply: \(x=4\) - step7: Substitute the value of \(x:\) \(y=-\frac{1}{2}\times 4-2\) - step8: Calculate: \(y=-4\) - step9: Calculate: \(\left\{ \begin{array}{l}x=4\\y=-4\end{array}\right.\) - step10: Check the solution: \(\left\{ \begin{array}{l}x=4\\y=-4\end{array}\right.\) - step11: Rewrite: \(\left(x,y\right) = \left(4,-4\right)\) Let's solve the system of equations step by step and find the solution. The system of equations is: 1. \( 2x + y = 4 \) 2. \( y = -\frac{1}{2}x - 2 \) ### Step 1: Solve the system of equations We can substitute the second equation into the first equation. From the second equation, we have: \[ y = -\frac{1}{2}x - 2 \] Substituting this into the first equation: \[ 2x + \left(-\frac{1}{2}x - 2\right) = 4 \] ### Step 2: Simplify the equation Now, simplify the equation: \[ 2x - \frac{1}{2}x - 2 = 4 \] Combine like terms: \[ \left(2 - \frac{1}{2}\right)x - 2 = 4 \] \[ \frac{4}{2}x - \frac{1}{2}x - 2 = 4 \] \[ \frac{3}{2}x - 2 = 4 \] ### Step 3: Solve for \( x \) Add 2 to both sides: \[ \frac{3}{2}x = 6 \] Multiply both sides by \( \frac{2}{3} \): \[ x = 4 \] ### Step 4: Solve for \( y \) Now substitute \( x = 4 \) back into the second equation to find \( y \): \[ y = -\frac{1}{2}(4) - 2 \] \[ y = -2 - 2 \] \[ y = -4 \] ### Final Solution The solution to the system of equations is: \[ (x, y) = (4, -4) \] ### Graphing While I cannot plot the graph directly, you can graph the two equations on a coordinate plane: 1. For \( 2x + y = 4 \): - When \( x = 0 \), \( y = 4 \) (point (0, 4)) - When \( y = 0 \), \( x = 2 \) (point (2, 0)) 2. For \( y = -\frac{1}{2}x - 2 \): - When \( x = 0 \), \( y = -2 \) (point (0, -2)) - When \( y = 0 \), \( x = -4 \) (point (-4, 0)) Plot these points and draw the lines to see where they intersect at the point \( (4, -4) \).