Question 33348
There are many ways to solve such equations.  You can either use substitution, or elimination, or Cramer's Rule to solve this.
I would Use Cramer's Rule to do so:
D = Determinant of [(1,-3,2);(2,-4,3);(3,-5,-4)] = 1(31)-2(22)+3(-1) = -16;
D(x) = Determinant of [(-11,-3,2);(-15,-4,3);(5,-5,-4)]
= -11(31)+15(22)+5(-1) = -341+330-5 = -16;
D(y) = Determinant of [(1,-11,2);(2,-15,3);(3,5,-4)]
= 1(45)-2(34)+3(-3) = 45-68-9 = -32;
D(z) = Determinant of [(1,-3,-11);(2,-4,-15);(3,-5,5)]
= 1(-95)-2(-70)+3(1) = -95+140+3 = 48;
x = D(x)/D = -16/-16 = 1;
y = D(y)/D = -32/-16 = 2;
z = D(z)/D = 48/-16 = -3;
Answer: (x,y,z) = (1,2,-3)