How many solutions does the system of equations have?
3x = -12y + 15 and x + 4y = 5
A-one
B-two
C-infinitely many
D-none
To determine the number of solutions, we can solve the system of equations.
First, let's solve the second equation for x:
x + 4y = 5
x = 5 - 4y
Then, substitute this value of x into the first equation:
3x = -12y + 15
3(5 - 4y) = -12y + 15
15 - 12y = -12y + 15
We can see that -12y terms cancel out, and we are left with 15=15.
Since the equation 15=15 is always true, this means the two equations are equivalent and represent the same line. Therefore, the system of equations has infinitely many solutions.
Answer: C-infinitely many.