HallsofIvy said:Seriously? Why did you not just put each of the given (x, y) pairs into the expressions and see which ones are correct?
rebo1984 said:There is no need to be rude.
Then why didn't you ask that question? As you phrased it, you seemed to be saying you had no idea how to do the arithmetic. That was why I said "Seriously?". I did not want to believe that you could NOT do the arithmetic- that would have been rude.I just wanted to know if there was another way of doing it.
rebo1984 said:It was rude and should not be condoned.
MarkFL said:I can appreciate that you may have felt put off by being asked "Seriously?", but since you didn't provide your thoughts or attempt at the problem, no one had any way of knowing that what you were after was a method besides direct substitution of the given ordered airs into the inequalities. Approaching a student with that question may not be what everyone would do, but I don't think it was meant in a discourteous way, but more as an expression of incredulity. I hope you can see now how your initial post, with no other information given, could evoke such a response. :D
We certainly do not condone rudeness from anyone, as our goal is to provide a friendly atmosphere where people can get math help. I've been doing this (giving math help on various sites) for quite a few years now, and HallsofIvy has been at it at least twice as long as I have. He has always provided good insightful help as long as I've been around, and I haven't seen where he is generally rude or uncivil. He has been recognized as a math help leader on every site on which he and I both participate, which speaks highly for how he is perceived by his math help peers and those to which he provides help. :D
Linear inequalities are mathematical expressions that compare two values using the symbols <, >, ≤, or ≥. They represent a range of possible values instead of a single solution.
To graph linear inequalities, you first plot the boundary line using the given inequality symbol (<, >, ≤, or ≥). Then, depending on whether the inequality is > or ≥, you shade the region above or below the line. If the inequality is < or ≤, you shade the region to the left or right of the line. The shaded region represents all possible solutions to the inequality.
The solution to a system of linear inequalities is the intersection of the solutions to each individual inequality. This can be represented graphically as the overlapping shaded regions on a graph.
To solve a system of linear inequalities algebraically, you must first solve each inequality for one of the variables. Then, you can use substitution or elimination to find the solution set of the system.
Solving systems of linear inequalities is commonly used in economics, such as in optimizing production and profit in a business. It can also be used in city planning to determine the best location for a new park or road, and in engineering to design structures that can withstand certain weight or force constraints.