Question 1205786
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x = number of hours to study for Chemistry
y = number of hours to study for Algebra
Both are nonnegative so {{{x>=0}}} and {{{y>=0}}}


x+y is the total number of hours studied
{{{x+y < 22}}} because he has less than 22 hours to study


{{{y >= 3x}}} since it takes him at least 3 times longer to study for Algebra than Chemistry.
Example: if he needs x = 4 hours for Chemistry, then he'll need at least 3x = 3*4 = 12 hours for Algebra.


The system of inequalities is 
{{{system(x>=0,y>=0,x+y<22,y>=3x)}}}


The first two inequalities tell us to focus on the upper right quadrant.
Inside this quadrant, we'll shade below the dashed line x+y = 22 and above the solid line y = 3x. 
The graph is shown at this Desmos link
<a href="https://www.desmos.com/calculator/23hbtoqjk1">https://www.desmos.com/calculator/23hbtoqjk1</a>


The corner points of this overlapped shaded region are:
(0,0)
(0,22)
(5.5, 16.5)
Each corner point is the result of intersecting the boundary lines. 
Eg: (5.5, 16.5) is the result of solving the system {{{system(x+y=22,y=3x)}}}


Be careful to note that points on the dashed boundary are NOT solutions; in contrast, points on the solid boundary are solutions.


Now onto the question "Can he spend 14 hours on Chemistry and 9 hours on Algebra?"
We have x = 14 and y = 9
x+y < 22
14+9 < 22
23 < 22
which is <font color=red>false</font>
Therefore he <font color=red>cannot</font> study Chemistry for 14 hours and Algebra for 9 hours.
The point (14,9) is not inside the shaded region.


You should find the same conclusion for the second question as well.
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