Question

X-2y+2z=15
2x-y-3z=-8
3x+2y-z=2
nilai x+y adalah

Answer 1

Pers 1 = x - 2y + 2z = 15
Pers 2 = 2x -y - 3z = -8
Pers 3 = 3x + 2y -z = 2
Pers 3 dan 1 pke sistem eliminasi y
3x + 2y -z = 2
x - 2y + 2z = 15
*karena nilai y sudah sma jdi langsung*
Hasilnya 4x + z = 17 (Hasil 1)
Pers 2 dan 3 pke sistem eliminasi y
2x - y - 3z = -8 | ×2 | 4x - 2y - 6z = -16
3x + 2y - z = 2 | × 1 | 3x + 2y - z = 2
Persamaan tdi d jumlah jdi hasilnya 7x - 7z = -14 (Hasil 2)
Hasil 2 dan 1 pke sistem eliminasi z
7x - 7z = -14 | ×1 | 7x - 7z = -14
4x + z = 17 | ×7 | 28x + 7z = 119
Hasil penjumlahannya 35x = 105
x = 105/35
x = 3
Subtitusikan nilai x ke hasil 1
4x + z = 17
4(3) + z = 17
12 + z = 17
z = 17 - 12
z = 5
Subtitusikan nilai x dan z ke pers 1
x - 2y + 2z = 15
3 - 2y + 2(5) = 15
3 - 2y + 10 = 15
-2y = 15 - 10 - 3
-2y = 2
y = 2/-2
y = -1

Jadi nilai x + y = 3 + (-1) = 2