How do you graph the system of linear inequalities #2x+y<6# and #y> -2#?

1 Answer
Alan P.
Apr 22, 2015

#2x+y<6# and #y > -2#
First consider the related linear equations:
#2x+y=6 rarr y = -2x+6#
and
#y = -2#

#y = -2x+6#
is a line with y-intercept at #(0,6)# and a slope of #(-2)# (which means that for every unit increase in #x#, #y# decreases by #2#)

#y=-2#
is a horizontal line through the point #(0,-2)#

It is fairly simple to plot these lines;
then we just need to determine which sides of these lines need to be combined for the given inequalities
Since
#y>-2#
the points of the Range must be above the horizontal line

Since
#2x+y<6#
the points of the Range must be below the line for #2x+y=6# (since if #y_1# is in the Range and #y_2<y_1# then #y_2# must also be in the Range).
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