Answer
$(3, 2, 2)$
Work Step by Step
A: $2x-3y+z=2$
B: $x-5y+5z=3$
C: $3x+y-3z=5$
3A+C
$3*(2x-3y+z)+3x+y-3z=2*3+5$
$6x-9y+3z+3x+y-3z=6+5$
$9x-8y=11$
3B+5C
$3*(x-5y+5z)+5(3x+y-3z)=3*3+5*5$
$3x-15y+15z+15x+5y-15z=9+25$
$18x-10y=34$
$9x-8y=11$
$18x-10y=34$
$-2*(9x-8y)+18x-10y=-2*11+34$
$-18x+16y+18x-10y=-22+34$
$6y=12$
$6y/6=12/6$
$y=2$
$9x-8y=11$
$9x-8*2=11$
$9x-16=11$
$9x=27$
$9x/9=27/9$
$x=3$
$3x+y-3z=5$
$3*3+2-3z=5$
$9+2-3z=5$
$11-3z=5$
$11=3z+5$
$6=3z$
$6/3=3z/3$
$z=2$
