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Sagot :
20x + 15y + 12z = 60 ⇒ 20x + 15y + 12z = 60
10x + 30y + 12z = 60 ⇒ 20x + 60y + 24z = 120
-45y - 12z = -60
-45y + 45y - 12z = -60 + 45y
-12z = -60 + 45y
-12 -12
z = 5 - 45/12y
20x + 15y + 12(5 - 45/12y) = 60
20x + 15y + 12(5) - 12(45/12y) = 60
20x + 15y + 60 - 45y = 60
20x + 15y - 45y + 60 = 60
20x - 30y + 60 = 60
-60 -60
20x - 30y = 0
20x - 20x - 30y = 0 - 20x
-30y = -20x
-30 -30
y = 2x/3
20x + 15(2x/3) + 12(5 - 45/12y) = 60
20x + 10x + 60 - 45y = 60
30x - 45y + 60 = 60
-60 -60
30x - 45y = 0
30x - 45y + 45y = 0 + 45y
30x = 45y
30 30
x = 3/2y
20(3/2y) + 15(2x/3) + 12(5 - 45/12y) = 60
30y + 10x + 60 - 45y = 60
10x + 30y - 45y + 60 = 60
10x - 15y + 60 = 60
-60 -60
10x - 15y = 0
10(3/2y) + 30(2x/3) + 12(5 - 45/12y) = 60
15y + 20x + 60 - 45y = 60
20x + 15y - 45y + 60 = 60
20x - 30y + 60 = 60
-60 -60
20x - 30y = 0
10x - 15y = 0 ⇒ 20x - 30y = 0
20x - 30y = 0 ⇒ 20x - 30y = 0
-60y = 0
-60 -60
y = 0
10x - 15(0) = 0
10x - 0 = 0
+0 +0
10x = 0
10 10
x = 0
20x + 15y + 12z = 60
20(0) + 15(0) + 12z = 60
0 + 0 + 12z = 60
0 + 12z = 60
12z = 60
12 12
z = 5
(x, y, z) = (0, 0, 5)
10x + 30y + 12z = 60 ⇒ 20x + 60y + 24z = 120
-45y - 12z = -60
-45y + 45y - 12z = -60 + 45y
-12z = -60 + 45y
-12 -12
z = 5 - 45/12y
20x + 15y + 12(5 - 45/12y) = 60
20x + 15y + 12(5) - 12(45/12y) = 60
20x + 15y + 60 - 45y = 60
20x + 15y - 45y + 60 = 60
20x - 30y + 60 = 60
-60 -60
20x - 30y = 0
20x - 20x - 30y = 0 - 20x
-30y = -20x
-30 -30
y = 2x/3
20x + 15(2x/3) + 12(5 - 45/12y) = 60
20x + 10x + 60 - 45y = 60
30x - 45y + 60 = 60
-60 -60
30x - 45y = 0
30x - 45y + 45y = 0 + 45y
30x = 45y
30 30
x = 3/2y
20(3/2y) + 15(2x/3) + 12(5 - 45/12y) = 60
30y + 10x + 60 - 45y = 60
10x + 30y - 45y + 60 = 60
10x - 15y + 60 = 60
-60 -60
10x - 15y = 0
10(3/2y) + 30(2x/3) + 12(5 - 45/12y) = 60
15y + 20x + 60 - 45y = 60
20x + 15y - 45y + 60 = 60
20x - 30y + 60 = 60
-60 -60
20x - 30y = 0
10x - 15y = 0 ⇒ 20x - 30y = 0
20x - 30y = 0 ⇒ 20x - 30y = 0
-60y = 0
-60 -60
y = 0
10x - 15(0) = 0
10x - 0 = 0
+0 +0
10x = 0
10 10
x = 0
20x + 15y + 12z = 60
20(0) + 15(0) + 12z = 60
0 + 0 + 12z = 60
0 + 12z = 60
12z = 60
12 12
z = 5
(x, y, z) = (0, 0, 5)
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