How do you solve #3x+y<=6#?

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Answer 1 · 2018-07-20T09:32:20

Please see the explanation below.

Solving linear inequalities in #2# variables is done graphically.

Any point lying in the shaded area, will comply to the inequality.

Take, for example, the point #(-5,2)# which is in the shaded area

Then,

#3x+y=3*-5+2=-13#

And this is #<=6#

Take, for example, the point #(5,5)# which is outside the shaded area

Then,

#3x+y=3*5+5=25 #

And

This does not comply to the conditions

#3x+y<=6#

graph{3x+y-6<=0 [-16.02, 16.01, -8.01, 8.01]}