6x -5y =20 and 5y - 6x = -20

A) No Solution
B) Infinity
C) A Point

Consistant or Inconsistant

Depdendant or Independant

The two equations are dependent. One can be derived from the other. There are an infinite number of (x,y) solutions.

To determine whether the given system of equations has a solution, we can solve it using the method of elimination. We will eliminate one variable by adding the two equations together.

When we add the equations "6x - 5y = 20" and "5y - 6x = -20," we get:
(6x - 5y) + (5y - 6x) = 20 + (-20)
6x - 5y + 5y - 6x = 0

As we can see, both the "x" and "y" variables cancel out, leaving us with 0 = 0. This equation is always true, regardless of the values of "x" and "y".

Therefore, the system of equations is consistent, meaning there is at least one solution. But since the equations are dependent on each other, all the points in the graph of one equation are also points in the graph of the other equation.

So, the correct answer is:
A) The system of equations has infinitely many solutions (Infinity).

Note: If the equations did not cancel each other and yielded an equation that was false (such as 7 = 0), the correct answer would be "No Solution" (A).