An algebra problem by Annie Li

Algebra Level 3

{ 2 x y 2 z = 3 x + 3 y + 2 = 1 5 x 4 y + 3 z = 10 \large \begin{cases} 2x - y -2z = -3 \\ x + 3y + 2 = -1 \\ 5x - 4y + 3z = 10 \end{cases}

Real numbers x x , y y and z z satisfy the system of equations above. What is x + y + z x + y + z ?


The answer is 1.

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1 solution

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)

I at first thought that there was a typo and that the second equation should be x + 3 y + 2 z = 1 x + 3y + 2z = -1 , which lead to an answer of x + y + z = 127 / 455 x + y + z = -127/455 , but when I just took the equations as given the answer did come out to 1 1 .

Brian Charlesworth - 4 years ago

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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.

Peter van der Linden - 4 years ago

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Wow I looked it again and the 2nd equation has no z... That's what I did wrong then.

Peter van der Linden - 4 years ago

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@Peter van der Linden Yes, Annie was trying to trick us. :)

Brian Charlesworth - 4 years ago

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