Graph the solution to the following system of inequalities.
4x+3y>-18
y<=-4/3x-2
Then give the coordinates of one point in the solution set.
point in the solution set - ( , )
To graph the solution to the system of inequalities, we first need to graph each individual inequality.
1. Graph the inequality 4x + 3y > -18:
To graph this inequality, we can start by finding two points on the line 4x + 3y = -18. We can set x = 0 and find the corresponding y-value, and then set y = 0 and find the corresponding x-value.
When x = 0, we have 4(0) + 3y = -18
3y = -18
y = -6
So one point is (0, -6).
When y = 0, we have 4x + 3(0) = -18
4x = -18
x = -4.5
So another point is (-4.5, 0).
Plot these two points and draw a dashed line through them, since the inequality is strict.
2. Graph the inequality y ≤ -4/3x - 2:
To graph this inequality, we can start by finding two points on the line y = -4/3x - 2. Again, we can set x = 0 and find the corresponding y-value, and then set y = 0 and find the corresponding x-value.
When x = 0, we have y = -4/3(0) - 2
y = -2
So one point is (0, -2).
When y = 0, we have 0 = -4/3x - 2
4/3x = -2
x = -3/2
So another point is (-3/2, 0).
Plot these two points and draw a solid line through them, since the inequality is inclusive of the equals sign.
Now, shade the region that satisfies both inequalities. The shaded region will be below the solid line and above the dashed line.
Finally, choose any point within the shaded region and provide its coordinates.
One point in the solution set could be (-1, -2).
Here is a rough sketch of the graph with the shaded region and one point labeled:
|
4 | . .
|
3 | .
| .
2 | .
| .
1 | .
|
0 |_____________________________
-6 -5 -4 -3 -2 -1 0 1 2