Penjelasan dengan langkah-langkah:

x + 2y + 2z = 60

x = 60 -2y -2z = Pers 1

Pers 1 di substitusi ke pers 2

3x + y + z = 65

3(60-2y-2z) + y + z = 65

180 -6y -6z + y + z = 65

180 -5y -5z = 65

-5y -5z = 65-180

-5y -5z = -115 = pers 4

Pers 1 di substitusi ke pers 3

2x + 3y - z = 45

2(60-2y-2z) + 3y -z = 45

120 -4y -4z + 3y -z = 45

120 -y -5z = 45

-y = 45 +5z -120

-y = -75 + 5z

y = 75 - 5z = Pers 5

Pers 5 di substitusi ke pers 4

-5y -5z = -115

-5(75 -5z) -5z = -115

-375 +25z -5z = -115

20z = -115 + 375

z = 260/20

z = 13

Nilai z di substitusi ke pers 4

-5y -5z = -115

-5y -5(13) = -115

-5y -65 = -115

-5y = -115 +65

-5y = -50

y = -50/-5

y = 10

nilai z dan y di substitusi ke pers 1

X = 60 - 2y -2z

X = 60 -2(10) -2(13)

X = 60 -20 -26

x = 14

Jawaban

X = 14

Y = 10

Z = 13

Bukti

x + 2y + 2z = 60

14 + 2(10) + 2(13) = 60

14 + 20 + 26 = 60

60 = 60

3x + y + z = 65

3(14) + 10 + 13 = 65

42 + 10 + 13 = 65

65 = 65

2x + 3y - z = 45

2(14) + 3(10) - 13 = 45

28 + 30 -13 = 45

45 = 45