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Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.5, x, plus, 6, y, equals, 45x+6y=410, x, plus, 12, y, equals, 810x+12y=8

Question

Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.5, x, plus, 6, y, equals, 45x+6y=410, x, plus, 12, y, equals, 810x+12y=8

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Solution

The given system of equations is:

  1. 5x + 6y = 4
  2. 10x + 12y = 8

First, let's simplify the second equation by dividing every term by 2:

5x + 6y = 4 5x + 6y = 4

Now, we can see that the two equations are identical. This means that they represent the same line in the coordinate plane.

Therefore, the system of equations has infinitely many solutions.

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