Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
3x + 2y = 9
-3x-2y-9
The given system of equations is:
3x + 2y = 9 (equation 1)
-3x - 2y = -9 (equation 2)
To determine the number of solutions, we can add equation 1 and equation 2 together. This will eliminate the y term and leave only the x term:
(3x + 2y) + (-3x - 2y) = 9 + (-9)
Simplifying:
0 = 0
Since 0 = 0, we can conclude that the system of equations has infinitely many solutions.