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 solve this system of equations, we will use the method of substitution or elimination.
Let's start with the first equation:
3x - 2y = 6
We can rearrange this equation to solve for x:
3x = 2y + 6
x = (2y + 6) / 3
Now, let's substitute this expression for x in the second equation:
5x = 5 - 25y
5((2y + 6) / 3) = 5 - 25y
Now we can solve for y:
(10y + 30) / 3 = 5 - 25y
Multiply both sides by 3 to eliminate the denominator:
10y + 30 = 15 - 75y
Rearrange the equation:
85y = -15
y = -15 / 85
Simplifying the expression:
y = -3 / 17
Now substitute this value of y back into the expression for x:
x = (2(-3 / 17) + 6) / 3
x = (-6 / 17 + 6) / 3
x = (6 - 6 / 17) / 3
x = (102 / 17 - 6 / 17) / 3
x = 96 / 17 / 3
x = (96 / 17) * (1 / 3)
x = 32 / 17
So, the solution to the system of equations is (32/17, -3/17).
Therefore, the correct answer is c) (32/17, -3/17).