Question

Tentukan nilai x-2y+4z dari persamaan x-2y+z=6 , 3x+y-2z=4 , 7x-6y-z=10 dengan metode eliminasi ?

Answer 1

Verified answer

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• eliminasi z
x - 2y + z = 6 || × 2
2x - 4y + 2z = 12

2x - 4y + 2z = 12
3x + y - 2z = 4
Jumlahkan
5x - 3y = 16 ... (1)

x - 2y + z = 6
7x - 6y - z = 10
Jumlahkan
8x - 8y = 16
x - y = 2 || × 3
3x - 3y = 6 ... (2)

5x - 5y = 10 ... (3)

• eliminasi y
5x - 3y = 16
3x - 3y = 6
Kurangkan
2x = 10
x = 5 ✔

• eliminasi x
5x - 3y = 16
5x - 5y = 10
Kurangkan
2y = 6
y = 3 ✔

x - 2y + z = 6
z = 6 - x + 2y
z = 7

•••
x - 2y + 4z = 5 - 2.3 + 4.7 = 27 ✔