# The number of non-negative integer solutions of the equations 6x + 4y + z = 200 and x + y + z = 100 is

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The number of non-negative integer solutions of the equations 6x + 4y + z = 200 and x + y + z = 100 is

(A) 3

(B) 5

(C) 7

(D) infinite

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The correct option is (C) 7.

The given equations are,

⇒  6x + 4y + z = 200  ---- (1)

⇒  x + y + z = 100  ---- (2)

x, y, z → Non − negative

z = 100 − (y + x) ≥ 0

Subtracting equation (2) from (1) we get,

⇒ 5x + 3y = 100

by (65 points) 1 flag
edited
option c  (20,0),(14,10),(8,20)
,(17,15),(11,15),(13,7),(5,25)