How do you solve #4x+2y<=80#?

2 Answers
Aug 24, 2015

Solving for #x#:
#x<=20-y/2#

Solving for #y#:
#y<=40-2x#

Explanation:

#4x+2y<=80#

Solved for #x#.

Subtract #2y# from both sides.

#4x<=80-2y#

Divide both sides by #4#.

#x<=80/4-(2y)/4#

#x<=20-1/2y##=#

#x<=20-y/2#

Solved for #y#.

Subtract #4x# from both sides.

#2y<=80-4x#

Divide both sides by #2#.

#y<=80/2-(4x)/2#

#y<=40-2x#

Aug 24, 2015

Solve the linear inequality in 2 variables : #4x + 2y <= 80#

Explanation:

Bring the inequality to standard form after simplification:
#2x + y - 40 <= 0.#(1)
First, graph the line 2x + y - 40 = 0 (2) by its 2 intercepts.
Make x = 0 --> y = 40. Make y = 0 --> x = 20.
Next, solve the inequality (1) by selecting the origin O as test point. Replace x = 0 and y = 0 into inequality (1). We get -40 <= 0. It's true then the solution set area contains O. It is the area below the line (2).
Color this area as answer.
Note . Because of the sign #(<=) #, the line (2) is included in the solution set.
graph{2x + y - 40 = 0 [-160, 160, -80, 80]}