a. Elimination method:
x + 2y + 5z = 12 |
7x - 3y + z = 16 | 7Row1-Row2 | 0x + 17y +34z = 68
-5x +7y + 9z = 9 | 5Row1-Row3 | 0x + 17y +34z = 69
0x + 0y + 0z = -1 [Row2 - Row3]
Because the statement 0x + 0y + 0z = -1 is false then the equations systems HAS NO SOLUTIONS.
b. Matrix analysis by determinant method:
| 1 2 5 |
| 7 -3 1 |
| -5 7 9 |
The determinant is 0 so the equations system has NO inverse, and HAS NO SOLUTIONS.
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