The solution is, there are infinitely many solutions to the system.
<h3>What is equation?</h3>
An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given:
3x - y + 4z = -10...(1)
-x + y + 2z = 6...(2)
2x - y + z = -8....(3)
From (1)
-y= -10-4z-3x
y= 10+4z+3x
from (2)
y=6-2z+x
equating above equations
10+4z+3x = 6-2z+x
4+6z+2x=0
x+3z+2=0
Now, from (3)
-y= -8-z-2x
y= 8+z+2x
again equating
6-2z+x = 8+z+2x
-2-3z-x=0
x+3z+2=0
As, both equations are same it is not possible to solve further.
Hence, there are infinitely many solutions to the system.
Learn more about this concept here:
brainly.com/question/14659401
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