Question 907028: Solve each system of inequalities by graphing
3x+4y>8
y<5x
I have no clue on how to solve this. Please show all your work so I can understand, thanks!
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!  means all the points to one side of the line represented by  , but not the points on that line.
(If it were  , then the points on that line would be included in the solution).
You graph that line as a dashed line to show that the line in just a boundary, but it is not part of the solution.
(If the line was part of the solution, you would graph it as a solid line).
To graph the line represented by (or any other line), you just need two points.
For , it is obvious that  makes  ---> ---> ,
so the point (0,2), with and is part of the line.
Another easy to graph point comes from making  .
In that case, the equation becomes
 ---> ---> ---> ---> ---> ,
and that tells you that the point (4,-1) is part of the line.
With the two points found, we can draw the line:
Since substituting the coordinates  (for point(0,0), the origin) makes the inequality not true,
the graph of is all the points on side of the line that does not include the origin, meaning all the points above that line (but not the points that are part of that line.
 means all the points to one side of the line represented by  , but not the points on that line.
The line is obviously the line that passes through points such as (-1,-5), (0,0) and (1,5),
and  than the points of the line represented by . That means all the points below that line.
 means the points common to the graphs and .
That means all the points in the angle between both lines that are above the graph for and below the graph for .
To indicate that you make the lines dashed and color or shade the angle:
 I drew the dashed lines in blue and shaded the angle in green.
|
|
|
