How to graph the system of inequalities

Question

Graph the system of inequalities and lable boundires. Use the graph to identify any two points that are solutions to the system. Explain work

The following is in a big bracket

y>1/4x-2

x+y<3 the < has a line under it

Answer 1

Hello, Lory from Idaho

 

For the first inequality:  1) Go to the Y- axis and plot a point on (0,-2)

                                   2) From (0,-2), move one unit up and then four to your right. 

                                        You should

                                       be at (-1, 4)

                                   3) Connect points (0,-2) and (-1, 4) with a BROKEN LINE. 

                                        It is broken because of the symbol >.

 

For the second inequality: I am going to make some changes, so I can graph it.  Here are the changes:

 x+y<=3

-x        -x

    y<=-x+3                 Now I am going to graph it as I did the previous inequality:

                                   1) Go to the Y-axis and plot (0,3)

                                   2) From (0,3) go down 1 and one to the right. So, you

                                       should be at (2, 1)

                                   3) Now, connect points (0,3) and (2,1) with a solid line. 

                                        The reason:  the symbol is <=.

 

If you graphed it carefully, the two inequalities should intersect at (4, -1).

 

Now, this part is going to be difficult to explain with out a graph, but I will try to be as thorough as possible. For the first inequality, y> 1/4X-2, shade up and to the left of the broken line.  The reason is that I am picking point (0,0) to see whether (0,0) will be in the shaded portion of this inequality or not.  In order to find that out, substitute 0 for x and 0 for y in this inequality.  so, we have (0)> 1/4(0)-2.  Or, 0>-2.  This is a true statement, so we need to shade the section of the inequality that contains the origin, (0,0).  Lets do the same to the second inequality to see which direction to shade.  x+y<=3 becomes 0+0<=3.  0<=3 is a true statement,  So, for the second inequality, you must shade down to the left.  Now, any point that is in the section where the two shading overlap, should be a solution to the problem  So, looking at the graph, (1,1), (1, -1) could be a set of points.  AGAIN, BECAREFUL with the BROKEN and SOLID lines. 

 

I hope this helps out and don't forget to rate my answer.

 

D. Y. T.