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Question 33570: please help me with this problem i have no idea how to get the answer and i have been working on it for an hour. solve the system of equations.
3x+4y+z=7
2y+z=3
-5x+3y+8z=-31
thank you!!!
Answer by mukhopadhyay(490)   (Show Source):
You can put this solution on YOUR website! 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)
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