tentukan himpunan penyelesaian dari SPLTV berikut dengan metode eliminasi a.) 2x - y = 1 2x + 3y = 5 b.) 7x -3y = 17 3x + 5y = 1 tentukan himpunan penyelesaian

1a)
2x - ....y = 1
2x + 3y = 5
----------------- -
-4y = -4
y = -4/-4
y = 1

2x - y = 1 (×3)
2x + 3y = 5 (×1)

6x - 3y = 3
2x + 3y = 5
----------------- +
8x = 8
x = 8/8
x = 1

Jadi HPnya adalah {1 , 1}


b)
7x - 3y = 17 (×3)
3x + 5y = 1 (×7)

21x - ...9y = 51
21x + 35y = ..7
---------------------- -
-44y = 44
y = 44/-44
y = -1

7x - 3y = 17 (×5)
3x + 5y = 1 (×3)

35x - 15y = 85
..9x + 15y = ..3
---------------------- +
44x = 88
x = 88/44
x = 2

Jadi HPnya adalah {2 , -1}


2)
3x - 2y + 4z = 10
4z = 10 - 3x + 2y
z = (10 - 3x + 2y)/4

4x - 2y + 5z = 14
4x - 2y + 5(10 - 3x + 2y)/4 = 14
16x/4 - 8y/4 + (50 - 15x + 10y)/4 = 14
(16x - 8y + 50 - 15x + 10y)/4 = 14
x + 2y + 50 = 14 × 4
x + 2y = 56 - 50
x + 2y = 6 (pers. I)

2x + 3y - 6z = -2
6z = 2x + 3y + 2
z = (2x + 3y + 2)/6

4x - 2y + 5z = 14
4x - 2y + 5(2x + 3y + 2)/6 = 14
24x/6 - 12y/6 + (10x + 15y + 10)/6 = 14
(24x - 12y + 10x + 15y + 10)/6 = 14
34x + 3y + 10 = 14 × 6
34x + 3y = 84 - 10
34x + 3y = 74 (pers. II)

x + 2y = 6
x = 6 - 2y

34x + 3y = 74
34(6 - 2y) + 3y = 74
204 - 68y + 3y = 74
-65y = 74 - 204
-65y = -130
y = -130/-65
y = 2

x = 6 - 2y
x = 6 - 2(2)
x = 6 - 4
x = 2

3x - 2y + 4z = 10
3(2) - 2(2) + 4z = 10
6 - 4 + 4z = 10
2 + 4z = 10
4z = 10 - 2
4z = 8
z = 8/4
z = 2

Jadi HPnya adalah {2 , 2 , 2}