Solve the following system of equations using Gaussian elimination or Gauss-Jordan elimination. Use a graphing calculator to check your answer. a+b-c=5 a-b+c=7 3a+b-c=-6 Select the correct choice below and, if necessary fill in the answer boxes to complete your choice. A. There is one solution. The solutior-is (square ,square ,square ) (Type integers or simplified fractions.) B. There are infinitely many solutions of the form (square ,square ,z) , where z is any real number. (Simplify your answers. Type expressions using z as the variable.) C. There is no solution

To solve the system of equations using Gaussian elimination, we first write the augmented matrix for the system: Step 1: Use row operations to get a leading 1 in the first row, first column (which is already done).Step 2: Eliminate the first column entries below the leading 1 by subtracting appropriate multiples of the first row from the other rows.- Subtract the first row from the second row: - Subtract 3 times the first row from the third row: The matrix now looks like this: Step 3: Use row operations to make the second row, second column entry a leading 1. Divide the second row by -2: The matrix now looks like this: Step 4: Eliminate the second column entries above and below the leading 1 in the second row.- Subtract the second row from the first row: - Add 2 times the second row to the third row: The matrix now looks like this: Since the last row corresponds to the equation , which is a contradiction, there is no solution to the system of equations.Therefore, the correct choice is:C. There is no solution.