Question

y ≥ -3x - 7
y < x + 5

Explanation:

Step1: Find the intersection point

Set $-3x - 7=x + 5$.
Solve for $x$:
\[

$$\begin{align*} -3x - 7&=x + 5\\ -3x-x&=5 + 7\\ -4x&=12\\ x&=- 3 \end{align*}$$

\]
Substitute $x = - 3$ into $y=x + 5$, then $y=-3 + 5=2$. The intersection point of $y=-3x - 7$ and $y=x + 5$ is $(-3,2)$.

Step2: Analyze the inequality $y\geq - 3x - 7$

The line $y=-3x - 7$ has a slope of $-3$ and a $y$-intercept of $-7$. Since $y\geq - 3x - 7$, the region is above (including the line) $y=-3x - 7$.

Step3: Analyze the inequality $y

The line $y=x + 5$ has a slope of $1$ and a $y$-intercept of $5$. Since $yThe solution of the system of inequalities is the region that satisfies both inequalities, which is the region that is above or on the line $y=-3x - 7$ and below the line $y=x + 5$.

Answer:

The solution of the system of inequalities $y\geq -3x - 7$ and $y