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# Graphs of systems of inequalities word problem

Given the graph of a two-variable linear inequality that models a context about chopping vegetables, Sal finds if there's enough time to chop!

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• Does this mean that carrots are cut at a rate of 540/30 and broccoli heads are cut at a rate of 540/15?
• Yes, although it probably wouldn't be literal in real life.
• At it is said carrots and broccoli take the same time to get cut but graph of inequality doesn't show it. It says 15 broccoli and 0 carrots can be cut in 540 seconds at the same time shows 30 carrots and 0 broccoli can be cut in 540 seconds.
Does this mean,
15 B + 0 C = 540 s
30 C + 0 B = 540 s

B= 36 s
C= 18 s
??
This contradicts the fact in the question
(1 vote)
• It actually says that it takes the same number of seconds to chop each carrot and the same number of seconds to chop each broccoli. This does not mean that the carrots and broccoli are chopped at the same rate, but that the rate of chopping carrots is constant (as you found 18 sec/carrot) and the rate of chopping broccoli is constant (36 sec/carrot).
• Q: How do you know which variable to assign to which axes.
I saw that the y axes was replaced by B and the x axes by C.
Why not have C be the y axes and B be the x axes?
• They both work! The nice thing about algebra is that you can make the axes whatever you want. Sometimes there are conventions (time is the x axis), but it doesn't matter which you use.
• Can someone plz help me on how the answer is 20? At , Why does Sal shade the overlap?
(1 vote)
• sal shades the overlap due to the property of inequalitites. when inequalitites are graphed and multiple inequalities are graphed, to find answers that satisfy all of the inequaitites you will need to shade in a particular part of the graph. to help remember how to graph these inequalities, remember:
< is a dashed line and shading below
> is a dashed line and shading above
≤ is a solid line and shading below
≥ is a solid line and shading above
• Could we have calculated equation B from the information given, or not? I noticed that it was given a y-int of 15 and x-int of 30 - this must have been using additional information? If not, I would appreciate any advice on how it could be calculated from the info given. Thanks.
(1 vote)
• I didn't understand inequality B and, how the line was graphed?
(1 vote)
• Arbaaz,

The point of this video is to discuss how to understand the graphed solution. There isn't really enough information written to determine how the line was graphed. We would need the number of seconds it takes to chop each type of vegetable to walk through graphing the line.
(1 vote)
• Why is it shaded blue if it says she wants to chop at least 20 vegetales? Should it not be below?
• Isaiah,

Think of it this way:

She wants to chop at least 20 vegetables - NOT less than 20 vegetables.

She wants to chop 20 vegetables or more.

Vegetables she wants to chop >= 20.
• Will it always be the intersection point?
(1 vote)
• Anoosha,

No, there will not always be an intersection point. There are times when the lines will be parallel, which makes the answer the empty set.
(1 vote)
• Wait so let me get this straight. The total number of vegetable has to be AT LEAST the constraint of 20, but she cannot cut anymore than this number multiplied by the given time it takes to cut each vegetable?