SOLUTION: does this system of equation have a unique solution? 7x-2y=15 -28x+8y=7

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Question 371206: does this system of equation have a unique solution?
7x-2y=15
-28x+8y=7
Found 3 solutions by nyc_function, jsmallt9, robertb:
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website!
This system of linear equations does not have a solution.
ANSWER = NO SOLUTION.

P.S. I worked out the math on paper.

Answer by jsmallt9(3758)   (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:

| 7 -2 | | -28 8 |

The value of this determinant is 7*8 - (-28)*(-2) = 56 - 56 = 0. Since this determinant is zero there is no unique solution. (If this determinant had worked out to be non-zero, then there would be a unique solution.)

Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website!
Getting a zero for the determinant of the coefficient matrix is not enough to say that it has no unique solution, or that it has no solution. To know which one is the real situation, you have to go back to the original system: The 2nd equation can be written as -4*(7x - 2y) = 7, or 7x - 2y = -7/4. Direct substitution into the top equation gives 15 = -7/4, a contradiction. Hence the system has no solution, or inconsistent.