If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

# Modeling with systems of inequalities

Sal models a real-world context into an algebraic system of linear inequalities and graphs it. Created by Sal Khan.

## Want to join the conversation?

• When Sal is drawing the coordinate system around , he takes a guess at which resolution to use on the axes. This is not a good way to do it. Better is to wait until the step he does around , that is, figure out the maximum values that g and s can take while still satisfying the second inequality. Had he done that, he would not have had an unused half of the coordinate space.

Actually, better is to figure out the values for both inequalities first, and then figure out how to best draw them.
• His stated goal is to solve by graphing, so it would be cheating for him to use algebra to find the answer and then solve by graphing!
Now if he wanted to publish his results somewhere, he would probably readjust his scales and use a graphing utility to give straight lines and perfect intercepts.
• Why are we able to make G equal to 0? I am having some trouble understand why and ho we make G or maybe y equal to zero? What is the process, why is it allowed?
• The condition specifies that you buy 15 ITEMS. Notice how it does not specify that you must buy one game or that you must buy 1 song. You just need to buy 15 items in total (which can mean having no songs or games), with the total bill being less than \$25. That is why g can be 0.

In this video, Sal sets g to 0, and then S to 0, is because he wants to find the s and g intercepts (i.e what the s value is when g is 0, and vice versa).
• Did he forget the 18 on the "s" axis or am I imagining things?
• He is moving in jumps of four
(1 vote)
• is this the same a linear programming ?
• This is a part of linear programming. The second part of linear programming is using the vertices of the unshaded area (On the graph in the video) to find the optimal value that can be obtained with use of an objective function.
• At why did you put g as zero? could it have been different like instead of zero could you have put five?
• You set g equal to zero and s equal to zero so you can form a line. With the second inequality he does the same thing, sets g equal to zero and s equal to zero so he can form a line. By finding the x and y intercepts of the inequality (by setting g and s equal to zero) you can then draw a line. By doing that, he can find out where the inequalities overlap where or where they share the same solution set). He could have converted both inequalities into slope intercept form and graphed the line but it's unnecessary because you can just draw a line from the inequalities given.
• I tried switching the axes by putting the games on the y-axis and songs on the x-axis. However, I got a different slope which resulted in a different answer. Why is this so? Can someone help please?
• Think of it this way. The normal formula for slope = change in Y / change in X
If you reversed the 2 axis, you would have change in X / change in Y
Your slope should be the reciprocal of Sal's slope.
Hope this helps.
• Wait, you can't have a fraction or portion of a game, so why didn't Sal round the number of games down..?

Ex.
• Samuel,

Sal didn't round at this point in the calculation because he is trying to find the x and y intercepts in order to plot the line. He is not looking for an exact answer.
• At , is it incorrect to switch the song axis and game axis? Does it matter which axis we have to put the variable on?
• You are correct. The choice of which axis should represent which variable was entirely arbitrary. Making the opposite choice would not have changed the problem.