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Solve the system by the method of your choice. {x = 4y + 2 −3x + 12y = −6 Select the correct choice below...

Solve the system by the method of your choice.
{x = 4y + 2
−3x + 12y = −6
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 = 4y + 2} or {(x,y)| −3x + 12y = −6}.
C. The solution set is ∅.

Answer

First, let's solve the system of equations:

  1. Equation 1: x = 4y + 2
  2. Equation 2: −3x + 12y = −6

Substitute x from Equation 1 into Equation 2:

−3(4y + 2) + 12y = −6

−12y − 6 + 12y = −6

−6 = −6

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 = 4y + 2} or {(x,y)| −3x + 12y = −6}.

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