Question 1208844
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x = number of hours worked at the grocery store
y = number of hours delivering newspapers


The two inequalities Mike would graph are
{{{system(x+y <= 20,7x+10y >= 90)}}}


The first inequality is the constraint where Mike is able to work at most 20 hours, i.e. 20 hours or fewer.
The other inequality is making his total earnings (7x+10y dollars) to be $90 or larger.
7x = amount earned just from the grocery store
10y = amount earned from delivering newspapers


The line x+y = 20 goes through (0,20) and (20,0). 
We shade below this line to graph {{{x+y <= 20}}}. This boundary line is solid because of the "or equal to".


The line 7x+10y = 90 goes through (0,9) and (10,2). We shade below above line to graph {{{7x+10y >= 90}}}. This boundary is also solid.


These two regions overlap to help form the solution set. 
This is denoted as region R shown below.
{{{
drawing(500,500,-5,25,-5,25,
graph(500,500,-5,25,-5,25,-100,-x+20,(90-7x)/10),
locate(4.5,10,"R")
)
}}}
x+y = 20 is the green line
7x+10y = 90 is the blue line


We focus only on the upper right quadrant where {{{x >= 0}}} and {{{y >= 0}}} since it makes no sense to have x or y be negative. 
Region R is a quadrilateral with these vertex points
(0,9), (0,20), (20,0), (12.8571, 0)
The decimal value is approximate.


A few selected points in region R would be:
(2, 13), (5, 10), and (9, 9)
I'll let the student verify each point with the constraint inequalities.


A point like (4,16) is on a solid boundary line, which means we include it as part of the solution set.


A point like (5,22) is not inside region R, and not on the boundary either, so it's not a solution point. 
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