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Solve by the method of your choice. 7x - 4y = 20 4x + y = 18 Select the correct choice below and, if...

Solve by the method of your choice.
7x - 4y = 20
4x + y = 18
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)|7x - 4y = 20} or {(x,y)|4x + y = 18}.
C. The solution set is ∅.

Answer

Solution: Solve the system of equations:

  1. 7x - 4y = 20
  2. 4x + y = 18

Multiply the second equation by 4 to eliminate y:

  1. 7x - 4y = 20
  2. 16x + 4y = 72

Add the equations:

23x = 92

x = 4

Substitute x = 4 into the second equation:

4(4) + y = 18

16 + y = 18

y = 2

The solution is (4, 2).

Correct choice: A. The solution set is {(4, 2)}.

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