Hello, I am having trouble understanding this question. I don\'t need the comple

Question

Hello, I am having trouble understanding this question. I don't need the complete step by step written I just need to be pointed at the right direction.

So, I have three questions, three varibales, yet one of them is defined by the other two. Meaning, I have an eqaution where x - 5 = xz and the another eqation where y - 6 = yz and then I have x^2 + y^2 = 8. I figured how to get the 1st set of values by simple pluggin numbers, however there are two solution to this problem .

So please, if you could just direct me in the right track, I would be thankful!

FYI numbers given are random.

Explanation / Answer

x - 5 = xz              (1)

y - 6 = yz               (2)

x^2 + y^2 = 8           (3)

divide eq 1 by x,

1 - 5/x = z

1 - z = 5/x

x = 5/(1-z)

Divide eq 2 by y,

1 - 6/y = z

1 - z = 6/y

y = 6/(1-z)

Plug value of x and y in eq 3,

[5/(1-z)]^2 + [6/(1-z)]^2 = 8

On solving,

25/(1-z)^2 + 36/(1-z)^2 = 8

(25+36)/(1-z)^2 = 8

61 = 8 + 8z^2 - 16z

8z^2 - 16z - 53 = 0

On solving,

z=-1.7,3.7

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