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Solve the system by the method of your choice. {x = 3y - 1 2x - 6y = -2} Select the correct choice below...

Solve the system by the method of your choice.
{x = 3y - 1
2x - 6y = -2}
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. There is exactly one solution. The solution set is { }. (Type an ordered pair.)
B. There are infinitely many solutions. The solution set is {(x,y)| x = 3y - 1} or {(x,y)| 2x - 6y = -2}.
C. The solution set is ∅.

Answer

Solution: Let's solve the system of equations:

  1. First equation: x = 3y - 1
  2. Second equation: 2x - 6y = -2

Substitute x from the first equation into the second equation:

2(3y - 1) - 6y = -2

6y - 2 - 6y = -2

-2 = -2

This is a true statement, indicating that the equations are dependent and represent the same line.

Answer: B. There are infinitely many solutions. The solution set is {(x,y)| x = 3y - 1} or {(x,y)| 2x - 6y = -2}.

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