Graph the solution of the system of linear inequalities.
y ≥ = - x + 2
y ≤ = 4x + 6
coordinates
Unfortunately, there seems to be a mistake in the inequalities provided. There are unnecessary equals signs after the inequality symbols.
To correctly graph the system of linear inequalities, we need to rewrite them as:
y ≥ -x + 2
y ≤ 4x + 6
First, let's graph the inequalities individually:
1. y ≥ -x + 2:
- Plot the y-intercept at (0, 2).
- Use the slope (-1) to find another point. For example, if x = 2, we have y = -2 + 2 = 0. Plot the point (2, 0).
- Draw a solid line passing through these two points since the inequality is greater than or equal to (≥).
- Shade the area above the line.
2. y ≤ 4x + 6:
- Plot the y-intercept at (0, 6).
- Use the slope (4) to find another point. For example, if x = 1, we have y = 4(1) + 6 = 10. Plot the point (1, 10).
- Draw a solid line passing through these two points since the inequality is less than or equal to (≤).
- Shade the area below the line.
The shaded regions from both inequalities will overlap, which represents the solution to the system of linear inequalities.
Here is a rough sketch of the graph:
```
|
10| P2|____
| | \
| | \
| | \
| | \
| | \
| P1____|________\_____
|
|
--------------------------------
0 1 2 3 4 5 6 7
```
Please note that the graph is not to scale and is only meant to provide a visual representation of the solution.