Chapter 2 - Matrices and Systems of Linear Equations - 2.3 Terminology for Systems of Linear Equations - Problems - Page 144: 4

See below.

Plugging in the values into the equations: $s+(s-2t)-(2s+3t)+5t=(s+s-2s)+(-2t-3t+5t)=0$ $2(s-2t)-(2s+3t)+7t=(2s-2s)+(-4t-3t+7t)=0$ $4s+2(s-2t)-3(2s+3t)+13t=(4s+2s-6s)+(-4t-9t+13t)=0$ All of the equations are satisfied, thus it is in fact a good solution.