What is the solution of the system of equations?
2 answers:
Answer:
The answer to your question is:
x = 4
y = -1
z = -3
Step-by-step explanation:
3 x + 2 y + z = 7
5 x + 5 y + 4 z = 3
3 x + 2 y + 3 z = 1
= 45 + 10 + 24 - (30 + 24 + 15)
= 79 - 69
Δ = 10
= 105 + 6 + 8 - (18 + 56 + 5)
= 119 - 79
Δx = 40
= 27 + 5 + 84 - ( 105 + 12 + 9)
= 116 - 126
Δy = -10
= 15 + 70 + 18 - (10 + 18 + 105)
= 103 - 133
= -30
Δz = -30
x = Δx /Δ = 40/10 = 4
y = Δy/Δ = -10/10 = -1
z = Δz/Δ = -30/10 = -3
Answer:
x = 4, y = -1 and z = -3.
Step-by-step explanation:
3 x + 2 y + z = 7 (A)
5 x + 5 y + 4 z = 3 (B)
3 x + 2 y + 3 z = 1 (C)
Subtract: A - C:
-2z = 6
z = -3.
Substitute for z in equations A and B:
3 x + 2 y - 3 = 7
3 x + 2 y = 10 (D)
5x + 5y = 15 (E)
Multiply D by -5 and E by 2:
-15x - 10y = -50
10x + 10y = 30 Adding these 2 equations:
-5x = -20
x = 4.
Finally Substitute x = 4 and z = -3 in equation C:
3(4) + 2y + 3(-3) = 1
2y = 1 - 12 + 9 = -2
y = -1.
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