Three planes

Geometry Level pending

If ( a , b , c ) (a,b,c) is the point of intersection of the planes 2 x + y − z = − 1 2x+y-z=-1 , x + y + z = 2 x+y+z=2 and 3 x − y − z = 6 3x-y-z=6 then what is the value of a + b + c a+b+c ?


The answer is 2.

Achraf Wassim by Achraf Wassim , 41, Egypt

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1 solution

Applying Kramer's rule to solve the three equations we get

x = 2 , y = − 2.5 , z = 2.5 x=2,y=-2.5,z=2.5 . So a = 2 , b = − 2.5 , c = 2.5 a=2,b=-2.5,c=2.5 , and a + b + c = 2 a+b+c=\boxed 2 .

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