## Question

###### How do you solve the system of inequalities #2x + 5y \leq - 20# and #- 5x + 4y > - 4#?

## Answers

It is that region that is below or on

#y=-2/5x-4# and at the same time above the plot#y=5/4x-1# . All as the shaded region on the graph.## Explanation:

It is that condition which satisfies both conditions.

Note that

#-5x+4y > -4# can never take on the value of -4 so by convention this condition is shown as a dotted line.

#color(blue)("Consider "2x+5y <=-20)# Solid line as it may take on the value of -20

To plot this line we manipulate as follows:

Subtract

#2x# from both sides

#5y<=-2x-20# Divide both sides by 5

#y<=-2/5x-4 # The feasible region for this:

Select any value#x# . Draw a vertical line through it.#y# may take on any value on that vertical line that is either on the plot of#y=-2/5x-4# or below it.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Consider "-5x+4y > -4)# Dotted line as it may not take on the value of -4

To plot this we manipulate as follows:

Add

#5x# to both sides

#4y > 5x-4# Divide both sides by 4

#y > 5/4x-1# The feasible region for this:

Select any value for

#x# . Draw a vertical line through it.#y# may take on any value that is above the plot#y=5/4x-1#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Consider the combined feasible regions")# It is that region that is below or on

#y=-2/5x-4# and at the same time above the plot#y=5/4x-1# . All as the shaded region on the graph.