Question 33570
Sorry to hear that you have been trying this for an hour.  Here it goes:
There are various ways to solve a system of linear equations.  They are: Elimination method, Substitution method, Cramer's Rule etc.  I would use Cramer's Rule to do this.
Determinant of the matrix = 3(16-3)-5(4-2) = 29;
Determinant of X = 7(16-3)-3(32-3)-31(4-2) = 91-87-62 = -58
Determinant of Y = 3(24+31)-5(7-3) = 165-20 = 145;
Determinant of Z = 3(-62-9)-5(12-14) = -213+10 = -193;
x = Determinant of X / Determinant of the matrix = -58/29 = -2;
y = Determinant of Y / Determinant of the matrix = 145/29 = 5;
z = Determinant of Z / Determinant of the matrix = -193/29 = -7;
Answer: (x,y,z) = (-2,5,-7)