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Question 48022: can someone please help me this equation I have tried to solve it but I keep getting the wrong answer I need for someone to show me how to graph it.
thanks.
Solve the following system of linear inequalities by graphing.
3x – y < 2
x + y > 2
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! OK, this is fairly simple to do...
Given 3x – y < 2 and x + y > 2, we need to plot the lines 3x–y=2 and x+y=2.
Re-arranging these gives us y=3x–2 and y=2-x, so plot these two. Hopefully you can do that? You will get 2 straight lines that cross at one point. The coordinates of that crossing is the solution to 3x–y=2 and x+y=2. However, your question has inequalities rather than equals signs so instead of 1 solution, we will have many solutions, contained within a region of the graph.
OK...explanation:
3x–y<2 becomes y>3x-2 by moving the terms around. We have just plotted y=3x-2, so y>3x-2 is that region where the y value of a point you pick is GREATER than the 3x-2 value. This is the region ABOVE the line.
x+y>2 becomes y>2-x by moving the terms around. We have just plotted y=2-x, so y>2-x is that region where the y value of a point you pick is GREATER than the 2-x value. Again, this is the region ABOVE the line.
What i do is shade out the regions i do NOT want, so for the first line, shade everything under it. Similarly, shade everything under the second line too. The region you have left that is unshaded is the region you want as your answer... should be the V shaped region above both lines.
This is a lot of writing for a maths question explanation, but i cannot do it any other way on here. Hope it helps.
jon.
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