SOLUTION: Use determinants to determine the number of solutions for each of the following systems.Do Not solve the systems. A)3x-y= -6 2x= 3y+2 B)3x-y=7 6x-2y=10

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Question 341500: Use determinants to determine the number of solutions for each of the following systems.Do Not solve the systems.
A)3x-y= -6
2x= 3y+2

B)3x-y=7
6x-2y=10

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Use determinants to determine the number of solutions for each of the following systems.Do Not solve the systems.
A)3x-y= -6
2x= 3y+2
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Rearrange:
3x-y = -6
2x-3y= 2
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Coefficient determinant: 3*-3-(-1*2) = -9+2 = -7
The x-determinant: -6*-3-(-1*2) = 18+6 = 24
The y-determinant: 3*2-(-6*2) = 6+12 = 18
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Ans: one solution
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B)
3x-y=7
6x-2y=10
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Coefficient determinant: 3*-2-(-1*6) = -6+6 = 0
Ans: no solution
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Cheers,
Stan H.