How many solutions does the system have?
12x−15y=18
4x−5y=6
Responses
no solution
no solution - no response given
one solution
one solution - incorrect
infinitely many solutions
infinitely many solutions - not selected, this is the correct answer
two solutions
show your work
To determine the number of solutions of the system, we can start by looking at the two equations:
12x - 15y = 18 (1)
4x - 5y = 6 (2)
We can rewrite equation (2) as 12x - 15y = 18, which is equation (1). This means that the two equations are actually the same line. Therefore, the system of equations has infinitely many solutions.
So, the correct answer is: infinitely many solutions.