Identify the solution(s) of the system of equations, if any.
3x-2y=6
5x=5-25y
a) (28/13, 3/13)
b) (-3/17, 32/17)
c) (32/17, -3/17)
d) (32/9, 7/3)
To find the solution(s) of the system of equations, we need to solve the system by either substitution or elimination.
Let's solve it using the elimination method. First, let's rewrite the second equation in standard form:
5x + 25y = 5
Now, we can multiply the entire equation by -2 to make the coefficient of y in both equations opposite:
-2(3x - 2y) = -2(6)
-6x + 4y = -12
Now, we can add the two equations together to eliminate the y-variable:
(3x - 2y) + (-6x + 4y) = 6 + (-12)
-3x + 2y = -6
Simplifying further, we obtain:
-3x + 2y = -6
-3x + 2y = -6
The two equations obtained are identical, which means they represent the same line. Therefore, there are infinitely many solutions to the system of equations.
The correct answer is not given among the options provided.