6. Systems of Linear Inequalities
Sign In
Inequalities:⎩⎪⎪⎪⎪⎨⎪⎪⎪⎪⎧10<x+yx+y<20y≥20.4x+25y<90
Graph:
We are also given three different constraints for the mass and cost of the ring. We can create inequalities from that information.
The mass must be more than 10 grams but less than 20 grams | There must be at least 2 grams of gold used | The total cost must be less than $90 |
10<x+y<20 | y≥2 | 0.4x+25y<90 |
We will follow the same process to graph the other inequalities. We have already found the boundary lines. We will use the same test point to determine where to shade.
Inequality | Solid or Dashed Line | True or False |
---|---|---|
x+y<20 | Dashed | 0+0<20 True |
y≥2 | Solid | 0≱2 False |
0.4x+25y<90 | Dashed | 0.4(0)+25(0)<90 True |
Now we can graph all of the inequalities and shade them appropriately.
The solution region is where all of the shading overlaps.