Chapter 2 - Systems of Linear Equations - 2.1 Introduction to Systems of Linear Equations - Exercises 2.1 - Page 63: 24

$(x,y,z)=(5t+2,2t-1,t)$; $t$ refers to a real number.

Consider $y-2z=-1 \implies y=2z-1$ Suppose $z=t$ This implies $y=2t-1$ Now, $x-3y+z=5 \implies x-3(2t-1)+t=5$ or, $x=5t+2$ Our result is : $(x,y,z)=(5t+2,2t-1,t)$; $t$ refers to a real number.