If [x + y + z; x + z; y + z] = [12; 7; 9], what are x, y and z?

Question 27

MediumOriginal question

If $\begin{bmatrix} x + y + z \\ x + z \\ y + z \end{bmatrix} = \begin{bmatrix} 12 \\ 7 \\ 9 \end{bmatrix}$ , what are $x$ , $y$ and $z$ ?

x = 5,\ y = 3,\ z = 4

Correct answerYour answer

x = 3,\ y = 5,\ z = 4

Correct answerYour answer

x = 3,\ y = 4,\ z = 5

Correct answerYour answer

x = 4,\ y = 5,\ z = 3

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

Equating elements: $x + y + z = 12$ , $x + z = 7$ and $y + z = 9$ .
The first minus the second gives $y = 5$ ; then $z = 9 - 5 = 4$ and $x = 7 - 4 = 3$ .

Worth noting

$x = 5,\ y = 3$ swaps $x$ and $y$ ; check it in $x + z = 7$ and it fails.

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