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

Question

asked Aug 13, 2022 183k views

1 Answer

Daniel Waechter · Answer 1 · 2022-08-18T19:39:11+0000

Answer:

The system of equations has no solution.

Explanation:

Let the following system of linear equations:

$x +2\cdot y + z = 6$ (1)

$2\cdot x + y + 2\cdot z = 6$ (2)

x + y + z = 5 (3)

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

x = 5 - y - z

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

$(5-y-z) +2\cdot y + z = 6$

$2\cdot (5-y-z)+y+2\cdot z = 6$

y = 1 (4)

y = 4 (5)

Which lead to a contradiction, since
$4\\e 5$ . Therefore, the system of linear equations has no solution.