Chapter 3 Linear Systems and Matrices - 3.4 Solve Systems of Linear Equations in Three Variables - 3.4 Exercises - Skill Practice - Page 182: 13

Infinitely many solutions.

Using elimination for the first two equations: $5x+y-z=6$ $x+y+z=2$ _______________________ $6x+2y=8$ $\rightarrow 2y=8-6x$ $\rightarrow y=4-3x$ Substitute $y=4-3x$ in the third equation: $3x+y=4$ $3x+4-3x=4$ $4=4$ We can conclude that the system has infinitely many solutions.