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 less than or equal to, minus, x, minus, 6
y≤−x−6
y, is greater than or equal to, one half, x, plus, 3
y≥
2
1
​
x+3

Answer 1

To graphically solve the system of inequalities, we will need to plot the lines corresponding to each inequality and shade the appropriate regions.

First, let's graph the line y = -x - 6. To do this, we plot the y-intercept at -6 (point (0, -6)), and then plot another point using the slope of -1 (down 1 unit for every 1 unit to the right). Connecting these two points will give us the line.

Next, let's graph the line y = 1/2x + 3. To do this, we plot the y-intercept at 3 (point (0, 3)), and then plot another point using the slope of 1/2 (up 1 unit for every 2 units to the right). Connecting these two points will give us the line.

Now, we shade the appropriate regions. Since y ≤ -x - 6, we shade below the line y = -x - 6. Since y ≥ 1/2x + 3, we shade above the line y = 1/2x + 3.

The solution set is the shaded region that satisfies both inequalities.

Coordinates of a point in the solution set: (-4, -10)

Here is a rough sketch of the solution on the set of axes:

```
|
+ | /
\ | /
\ | /
\ | /
\ | /
\ | /
\|/
--------(-------)-------
/ | \
/ | \
/ | \
/ | \
/ | \
+ | /
|
```

The shaded region below the line y = -x - 6 and above the line y = 1/2x + 3 represents the solution set. The coordinates of a point in the solution set are (-4, -10).