Possible or Impossible?
⎩ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎧ x + y + z − 3 = 0 x − y + z + 1 = 0 x + y − z − 1 = 0 x − y − z + 3 = 0
Is it possible for x , y , z to satisfy the system of the equations above?
Bonus : If it is possible, give your answer as the sum of the values of x , y , z .
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3 solutions
@Mahdi Raza , did you read the question - you're supposed to give the answer as 1 or 0 .
Also, attempt the bonus...
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The answer can only be 1 or 3
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You can't have both, so better remove the bonus part
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@Mahdi Raza – No, the bonus is if it's possible. I should've put - give your answer to the Bonus in the discussion...
Solving the first three equations using Kramer's rule, we get x = 0 , y = 2 , z = 1 . Substituting in the fourth, we see that this equation is satisfied by these values of the unknowns.
@Alak Bhattacharya , can you show us how you used Cramer's rule to solve the first three equations?
x = 0 , y = 1 , z = 2
Not to be rude @Páll Márton , but you need to show how you got the solution.
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Same way as @Mahdi Raza
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He got y = 2 , z = 1 ...
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@A Former Brilliant Member – Ok, I misspelled :)
@A Former Brilliant Member – That is because y and z are symmetric here
( 2 ) + ( 3 ) ⟹ 2 x = 0 ⟹ x = 0
( 1 ) + ( 3 ) ⟹ 2 x + 2 y = 4 ⟹ y = 2
Substitute in any equation ⟹ z = 1
We see that it a solution is possible, thus the answer to be inputted is 1