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Pertanyaan

Jika (b+c, b-c) memenuhi sistem persamaan 3x - y + 2z = -1 dan -2x + y + 3z = -3, maka nilai b + c adalah ...

A. 0
B. 1
C. 2
D. 3
E. 4

1 Jawaban

  • 3x-y+2z=0 (subs (b+c , b-c)
    3(b+c)-(b-c)+2z=0
    3b+3c-b+c+2z=0
    2b+4c+2z=0

    -2x+y+3z=0 (subs (b+c, b-c))
    -2(b+c)+(b-c)+3z=0
    -2b-2c+b-c+3z=0
    -b-3c+3z=0

    2b+4c+2z=0 (×1) > 2b+4c+2z=0
    -b-3c+3z=0 (×2) > -2b-6c+6z=0
    -------------------(+)
    -2c+8z=0 > c= 4z
    -b-3c+3z=0 > -b-3(4z)+3z=0 > -b-12z+3z=0 > -b-9z=0
    b= -9z

    b:c
    -9z:4z
    -9:4
    b+c= -9+4=-5

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