Voldemort

Nice problem! 
Adding all the equations gives us

3(w + x + y + z) = 13

w + x + y + z = 13/3

The first equation becomes(Can you see how I did this?):

(w + x + y + z) - z = -2

Doing this step and solving the other variables, can you continue from here? 

Very interesting problem, indeed. I saw this problem on a textbook and the solution was very intriguing. 

Suppose we flip n choose k with n choose n - k...

This tuns the expression into:

$n*\binom{n}{0}+(n-1) \binom{n}{1}+…+0 \binom{n}{n}$

We can combine the (n k) terms with the (n n-k) terms to get n as the coefficient and multiply it by two because by combining, we halved the amount of terms. 

This gives us:
$n*\binom{n}{0}+(n) \binom{n}{1}+…+n \binom{n}{n}$

Note that if we factor out n on the left side, we get 2^n as the inside term(Make sure you know why) and n. But because we have multiplied the expression by two earlier, we have to divide it by two to get its true value. This gives us:

$n2^{n-1}$

So @BigBrain, I think there was a slight error. 

This forum is not a free platform for you to cheat and get free answers. I will leave this up for you to solve. 

f(x) = (5x-3)(5x-3) 

There are two roots of 3/5.

Therefore, 3/5 is the repeated root. 

I am not going to answer your question because you will have to solve it yourself. Based on the way I solved a similar question, you should have a an idea. Could you please explain your work so far?

If you have no progress made, then consider what makes both equations have an infinite set of solutions. 

The equilateral triangle will each have side lengths of 16 and the square will have all its side lengths of 12.

The area of the square is 12^2

We know that the altitude of the equilateral triangle is 8sqrt(3) by the 30-60-90 we form when dividing the triangle in half. Therefore, the area of the eqilateral triangle is 64sqrt(3)

Therefore, the ratio will be 

64sqrt(3)/144, which simplifies to 4sqrt(3)/9