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Math Asked by a SnapAndSolve user · about 2 hours ago

Solve by using substitution or elimination by addition. 5x - 4y = 5 -10x + 8y = -10 Select the correct...

Solve by using substitution or elimination by addition.
5x - 4y = 5
-10x + 8y = -10
Select the correct choice below and fill in any answer boxes present.
A. The unique solution to the system is (Type an ordered pair)
B. There are infinitely many solutions.
C. There is no solution.

Answer

First, let's simplify the system of equations:

  1. 5x - 4y = 5
  2. -10x + 8y = -10

Notice that the second equation is exactly -2 times the first equation:

  1. 5x - 4y = 5
  2. -2(5x - 4y) = -2(5)

This simplifies to:

  1. 5x - 4y = 5
  2. -10x + 8y = -10

Since the second equation is a multiple of the first, the two equations are dependent and represent the same line. Therefore, there are infinitely many solutions.

B. There are infinitely many solutions.

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