How do you graph the solutions to the system #y+2x<=0, 6x-5y<=15, y>= -8#?

1 Answer
Cesareo R.
Dec 29, 2016

See below.

Explanation:

Calling #s_1 ge 0, s_2 ge 0, s_3 ge 0# slack variables, we have

#{(y+2x+s_1 = 0),(6x-5y+s_2=0),(y-s_3 = -8):}#

Solving for #x,y,s_1# we obtain

#x=1/6(5(s_3-5)-s_2), y=s_3-8,s_1=1/3(49+s_2-8s_3)#

To have #s_1 ge0# suffices #49+s_2-8s_3 ge 0# or
#s_2 ge 8s_3-49# and this is attained if #8s_3-49 ge 0#
so finally if #s_3 ge 49/8=>s_2 ge 0=>s_1 ge 0# so the system has solutions

Attached a plot showing in light blue the feasible region.

enter image source here

Related questions
See all questions in Linear Inequalities in Two Variables
Impact of this question
1312 views around the world
You can reuse this answer
Creative Commons License