Question

solve the following system of inequalities graphically on the set of axes below. state the coordinates of a point in the solution set.
y ≥ -3x - 7
y < x + 5

Explanation:

Step1: Graph the line $y = - 3x-7$

The line $y=-3x - 7$ has a y - intercept of - 7 and a slope of - 3. Since the inequality is $y\geq - 3x-7$, the line is solid and we shade above the line.

Step2: Graph the line $y=x + 5$

The line $y=x + 5$ has a y - intercept of 5 and a slope of 1. Since the inequality is $y\lt x + 5$, the line is dashed and we shade below the line.

Step3: Find a point in the solution set

To find a point in the solution set, we can test a point. Let's test the point $(0,0)$.
For $y\geq - 3x-7$, when $x = 0$ and $y = 0$, we have $0\geq-3(0)-7= - 7$ (True).
For $y\lt x + 5$, when $x = 0$ and $y = 0$, we have $0\lt0 + 5=5$ (True). So $(0,0)$ is in the solution set.

Answer:

A point in the solution set is $(0,0)$