Question 371207: does this system have a unique solution? yes or no?
20x+5y=33
-32x+8y=47 Found 2 solutions by nyc_function, jsmallt9:Answer by nyc_function(2741) (Show Source):
You can put this solution on YOUR website! Since you posted this problem under "Matrices and Determinants" I assume you know what they are.
The fast way to determine whether or not there is a unique solution is to find the value of the following determinant:
| 20 5 |
| -32 8 |
The value of this determinant is 20*8 - (-32)*5 = 160 + 160 = 320. Since this determinant is non-zero there is a unique solution. (If this determinant had worked out to be zero, then there would not be a unique solution.)
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