An algebra problem by Annie Li
⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 2 x − y − 2 z = − 3 x + 3 y + 2 = − 1 5 x − 4 y + 3 z = 1 0
Real numbers x , y and z satisfy the system of equations above. What is x + y + z ?
The answer is 1.
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1 solution
I at first thought that there was a typo and that the second equation should be x + 3 y + 2 z = − 1 , which lead to an answer of x + y + z = − 1 2 7 / 4 5 5 , but when I just took the equations as given the answer did come out to 1 .
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Hmm. I have to find out what I did wrong then. I did use my calculator to check my calculations, so I went wrong somewhere else.
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Wow I looked it again and the 2nd equation has no z... That's what I did wrong then.
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@Peter van der Linden – Yes, Annie was trying to trick us. :)
Uhm I had a lucky guess with 1, because I believe the answer is a 1/13. With matrix calculation I find A^-1 x (x y z) = (-5/65 - 97/65 124/65)