solve the system of inequalities by graphing.\n$x > -4$\n$y < 2x + 4$\nselect a line to change it between…

Explanation:

Step1: Identify the first inequality boundary

The first inequality is $x > -4$. The boundary is a vertical line at $x = -4$. $$x = -4$$

Step2: Determine line style and shading for $x > -4$

Since the inequality is strictly "greater than", use a dashed line. Shade the region to the right. $$\text{Dashed line at } x = -4, \text{ shade right.}$$

Step3: Identify the second inequality boundary

The second inequality is $y < 2x + 4$. The boundary is a line with slope $2$ and y-intercept $4$. $$y = 2x + 4$$

Step4: Determine line style and shading for $y < 2x + 4$

Since the inequality is strictly "less than", use a dashed line. Shade the region below the line. $$\text{Dashed line through } (0, 4) \text{ and } (-2, 0), \text{ shade below.}$$

Step5: Find the intersection of shaded regions

The solution is the overlapping region where $x > -4$ and $y < 2x + 4$. $$\text{Intersection of right of } x = -4 \text{ and below } y = 2x + 4.$$

Answer:

To solve the system:

1. Draw a dashed vertical line at $x = -4$.
2. Draw a dashed line passing through $(0, 4)$ and $(-2, 0)$ for the equation $y = 2x + 4$.
3. Shade the region that is simultaneously to the right of the line $x = -4$ and below the line $y = 2x + 4$.