Question

Tentukan himpunan penyelesaian dari sistem persamaa linear berikut!
a) 2x-y+z=4
x+y-2z=-3
x+3y=z

Answer 1

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


x + y - 2z=-3|x3| 3x + 3y -6z = -9
 x + 3y - z= 0|x1| x + 3y -z = 0
                         ----------------------  -
                         2x - 5z = 9

3x - z = 1|x5| 15x - 5z = 5
2x - 5z = 3 |x1| 2x - 5z = 3
                       --------------- -
                       13x = 2
x = 2/13
2x - 5z = 3
2 ( 2/13) - 5z = 3
4/13 - 5z = 3
-5z = 3 - 4/13
-5z = 39 - 4/13
z = 35/13 x -1/5
z = -7/13

x+y-2z=-3
2/13 + y - 2(-7/13) = -3
2/13 + y + 14/13 = -3
16/13 + y = -3
y = -3 - 16/13
y = -39 - 16/13
y = -55/13