Answer: No Solutions exist
Step-by-step explanation:
We have the following system of equations

Rewriting the second equation we have:

Now we multiply the first equation by -3 and add it to the second equation

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Equality is not satisfied. Then the system has no solution
Unfortunately, Katie will be $20 short
She has $40
Plus the $38 x 5 she will be earning which is $190
$190+$40 is $230
Looks like Kate needs one more day of hard work to get her bike ; )
There are 9 diagonals.
Please see the attached picture for all the vertices that are drawn. When you start drawing the diagonals, be cautious of the ones that you have already drawn.