Question

Tentukan himpunan penyelesaian dari sistem persamaan berikut ini


a) x - 2y + z = 7
2x + 3y - z = 7
x + y + z = 4

b) 3x - y = 7
x + z = 7
x + y = z

(Dengan cara)

Answer 1

A)
x - 2y + z = 7
2x + 3y - z = 7
x + y + z = 4
=> (1) x-2y+z = 7
2x+3y-z = 7 +
_________
3x + y = 14 (4)
(2) 2x+3y-z = 7
x+y+z = 4 +
_______
3x + 4y = 11 (5)
(3) 3x+y = 14
3x+4y = 11 -
________
-3y = 3 => y = -1
(4) 3x + y = 14 => 3x - 1 = 14
=> 3x = 15 => x = 5
(5) x+y+z = 4 => 5-1+z = 4 => 4+z = 4
z = 0
HP = {5,-1,0}

b)
3x - y = 7
x + z = 7
x + y = z
=> (1) 3x-y = 7
x+y = z +
______
4x = 7 + z => 4x - z = 7
(2) x + z = 7
4x - z = 7 +
_______
5x = 14 => x = 14/5
(3) 3x - y = 7
3(14/5) - y = 35/5 => 42/5 - y = 35/5
=> y = 7/5
(4) x + y = z => 14/5+7/5 => z = 21/5
HP = {14/5, 7/5, 21/5}