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Solve the system by the method of your choice. 6x = y - 6 6x - y = 3 Select the correct choice below and,...

Solve the system by the method of your choice.
6x = y - 6
6x - y = 3
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The solution set is { }. (Type an ordered pair.)
B. There are infinitely many solutions. The solution set is {(x,y)|6x = y - 6} or {(x,y)|6x - y = 3}.
C. The solution set is ∅.

Answer

Solution:

  1. Given the equations:
  2. 6x = y - 6
  3. 6x - y = 3
  4. Rearrange the first equation: y = 6x + 6
  5. Substitute y in the second equation: 6x - (6x + 6) = 3
  6. Simplify: -6 = 3, which is a contradiction.
  7. Therefore, there is no solution.

Answer: C. The solution set is ∅.

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