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, is greater than, minus, 3, x, minus, 3
y>−3x−3
y, is greater than, x, minus, 7
y>x−7

Answer 1

Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.
y, is less than, minus, start fraction, 3, divided by, 2, end fraction, x, minus, 7
y<−
2
3
​
x−7
y, is less than, one half, x, plus, 1
y<
2
1
​
x+1

Answer 2

Here is the graph of the system of inequalities:

First, let's graph the line y = -3x - 3.
To do this, we can start by graphing the line y = -3x, which has a y-intercept of 0 and a slope of -3. Then, we can shift the line downward by 3 units by moving each point on the line down 3 units.

Next, let's graph the line y = x - 7.
To do this, we can start by graphing the line y = x, which has a y-intercept of 0 and a slope of 1. Then, we can shift the line downward by 7 units by moving each point on the line down 7 units.

Now, we need to shade the region above the line y = -3x - 3 and above the line y = x - 7.
The shaded region represents the solution set of the system of inequalities.

A point in the solution set is (1, -2) since it's located in the shaded region.

Here is the graph:

|
x |
-10 | . . . . . .
| /
-9 | . . . . .
| /
-8 | . . . .
| /
-7 | . . .
| /
-6 | . .
|/
-5 | .
--------------
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8

Answer 3

Here is the graph of the system of inequalities:

First, let's graph the line y = (3/2)x - 7.
To do this, we can plot two points on the line. For example, when x = 0, y = -7, and when x = 2, y = -4. We can then connect these two points to graph the line.

Next, let's graph the line y = (1/2)x + 1.
To do this, we can plot two points on the line. For example, when x = 0, y = 1, and when x = 2, y = 2. We can then connect these two points to graph the line.

Now, we need to shade the region below the line y = (3/2)x - 7 and below the line y = (1/2)x + 1.
The shaded region represents the solution set of the system of inequalities.

A point in the solution set is (4, -2) since it's located in the shaded region.

Here is the graph:

|
x |
-10 |
|
-8 | .
| |
-6 | . | . . .
| | |
-4 | . | |
| | | |
-2 | | | |
| | | |
0 |_____________
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8