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Solve the system by the addition method. 2x = 3y + 4 6x = 5 - 2y Select the correct choice below and, if...

Solve the system by the addition method.
2x = 3y + 4
6x = 5 - 2y
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. Use integers or fractions for any number in the expression.)
B. There are infinitely many solutions.
C. There is no solution.

Answer

First, let's rewrite the equations in standard form:

  1. 2x - 3y = 4
  2. 6x + 2y = 5

To use the addition method, we need to eliminate one of the variables. Let's eliminate x by making the coefficients of x in both equations equal:

  1. Multiply the first equation by 3: 6x - 9y = 12
  2. The second equation is already: 6x + 2y = 5

Now subtract the second equation from the first:

  1. (6x - 9y) - (6x + 2y) = 12 - 5
  2. -11y = 7
  3. y = -7/11

Substitute y = -7/11 back into the first equation:

  1. 2x - 3(-7/11) = 4
  2. 2x + 21/11 = 4
  3. 2x = 4 - 21/11
  4. 2x = 44/11 - 21/11
  5. 2x = 23/11
  6. x = 23/22

The solution set is (23/22, -7/11).

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