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Question 56343: Solve each of the following systems of linear inequalities graphically.
3x-y<6
x>1
y<3
NOTE each of the < or > signs are underlined, I did not know how to type this. Thanks so much. These are extreme problems!!!!!
McGraw Hill 6th edition. 8.4 # 10
Answer by aujla(1)   (Show Source):
You can put this solution on YOUR website! Graph each of the 3 equations.
y<=3 (this is y is less than or equal to 3)
this graph looks like a straight horizontal line, that crosses at y=3.
the area we are interested in is the area below this line. this is all points where y is less than or equal to 3.
X>=1 (this is x is greater than or equal to 1)
this graph looks like a stright vertical line, that crosses at x=1.
the area we are interested in is the area to the right of this line. this is all points where x is greater than or equal to 1. shade this area.
3x-y<6
this can be rerranged to y > 3x-6
this graph looks like a straight diagonal line, that crosses at y = -6 and x = 3.
the area we are interested in is the area above this line. this is all points where y is greater than or equal to 3x-6.shade this area.
you should get a triangle which satisfies all the equations, ie, a triangle shaded in 3 times.shade this area. this triangle, represents points, (ie, values of x and y ,that satisfy ALL 3 linear inequalities)
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