Question

Tentukan himpunan penyelesaian dari sistem persamaan
{X + 2x + z = 4
{2x + y + z= 4
{3x + y - z = 3

Answer 1

Verified answer

X + 2y + z  = 4
2x + y + z = 4
3x + y - z = 3

(3x + y - z) - (2x + y + z) = 3 - 4
3x - 2x + y - y - z - z = -1
x - 2z = -1
x = 2z - 1

x + 2y + z = 4
2z - 1 + 2y + z = 4
2y + 3z = 4 + 1
2y + 3z = 5

2x + y + z = 4
2(2z - 1) + y + z = 4
4z - 2 + y + z = 4
5z + y = 4 + 2
5z + y = 6
y = 6 - 5z

2y + 3z = 5
2(6 - 5z) + 3z = 5
12 - 10z + 3z = 5
-7z = 5 - 12
-7z = -7
7z = 7
z = 7/7
z = 1

y = 6 - 5z
y = 6 - 5(1)
y = 6 - 5
y = 1

x = 2z - 1
x = 2(1) - 1
x = 2 - 1
x = 1

jadi, himpunan penyelesaiannya adalah :
x = 1
y = 1
z = 1