SOLUTION: The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the system, if a solution exists.

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Question 1196103: The system of equations may have a unique solution, an infinite number of solutions, or no solution. Use matrices to find the general solution of the system, if a solution exists. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answers in terms of z as in Example 3.)

3x−2y+5z=8
2x−3y+4z=15
(x, y, z) =

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
system%283x-2y%2B5z=8%2C%0D%0A2x-3y%2B4z=15%29



To make the 2 on row 2 column 1 become 0,
 
-2R1+3R2->R2



To make the -2 on row 1 column 2 become 0,

-2R2+5R1->R1


To make the leading coefficients become 1,

(1/15)R1->R1
(-1/5)R2->R2



system%281x%2B0y%2Bexpr%287%2F5%29z=-6%2F5%2C+0x%2B1y-expr%282%2F5%29z=-29%2F5%29

system%28x%2Bexpr%287%2F5%29z=-6%2F5%2C+y-expr%282%2F5%29z=-29%2F5%29

system%28x=-6%2F5-expr%287%2F5%29z%2C+y=-29%2F5%2Bexpr%282%2F5%29z%29

%28matrix%281%2C5%2C+++x%2C%22%2C%22%2Cy%2C%22%2C%22%2Cz%29%29%22%22=%22%22

Edwin