Answered

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4/4 pts
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---the system of simoultanious equation
X+2y+z=6
2x+y+2z=6
X+y+z=5​

Sagot :

xero099

Answer:

The system of equations has no solution.

Step-by-step explanation:

Let the following system of linear equations:

[tex]x +2\cdot y + z = 6[/tex] (1)

[tex]2\cdot x + y + 2\cdot z = 6[/tex] (2)

[tex]x + y + z = 5[/tex] (3)

Since the quantity of equations and variables are the same, there is only one solution to this system. First, we clear [tex]x[/tex] in (3):

[tex]x = 5 - y - z[/tex]

And make substitution both in (1) and (2):

[tex](5-y-z) +2\cdot y + z = 6[/tex]

[tex]2\cdot (5-y-z)+y+2\cdot z = 6[/tex]

[tex]y = 1[/tex] (4)

[tex]y = 4[/tex] (5)

Which lead to a contradiction, since [tex]4\ne 5[/tex]. Therefore, the system of linear equations has no solution.

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