Chapter 2 - Matrices and Systems of Linear Equations - 2.3 Terminology for Systems of Linear Equations - Problems - Page 144: 3

See below.

Plugging in the values into the equations: $(1-t)+(2+3t)+(3-2t)=(1+2+3)+(-t+3t-2t)=6$ $(1-t)-(2+3t)-2(3-2t)=(1-2-6)+(-t+-3t+4t)=-7$ $5(1-t)+(2+3t)-(3-2t)=(5+2-3)+(-5t+3t+2t)=4$ All of the equations are satisfied, thus it is in fact a good solution.