Chapter 9 - Systems and Matrices - Summary Exercises on Systems of Equations - Exercises - Page 907: 12

$\{(2,-5,3)\}$

1. The first equation gives $x=-5y-23$ 2. Use it in the third equation to get $2(-5y-23)+5z=19$ or $-10y+5z=65$ or $-2y+z=13$ 3. Multiply 2 to the above and add the result $-4y+2z=26$ to the second equation to get $-z=-3$, thus $z=3$ 4. Back substitute to get $-2y+3=13, y=-5$ and $x=-5(-5)-23=2$ 5. Thus the solution set is $\{(2,-5,3)\}$