# geometry

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if x+y=11, y+z=14, and x+z=13, what is the value of x+y+z ?

• geometry -

Eq1: X + Y = 11.

Eq2: Y + Z = 14.
Y = 14 - Z.

Eq3: X + Z = 13.
X = 13 - Z.

In Eq1, substitute (13-Z) for X, and
(14-Z) for Y:
(13-Z) + (14-Z) = 11,
13 - Z + 14 - Z = 11,
-2Z + 27 = 11,
-2Z = 11 - 27 = -16,
Z = 8.

X + Y + Z,
Substitute 11 for y and 8 for Z:
(X+Y)+Z = 11 + 8 = 19.

• geometry -

CORRECTION:
Substitute 11 for (x+y).

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