How many solutions does the system have?
12x−15y=18
4x−5y=6(1 point)
Responses
two solutions
one solution
infinitely many solutions
no solution
To determine the number of solutions for the given system, we can use the method of elimination or substitution. Let's use the method of elimination:
First, we multiply the second equation by 3 to make the coefficients of y in both equations match:
3(4x - 5y) = 3(6)
12x - 15y = 18
We can see that both equations are now the same, meaning they are equivalent. Therefore, these equations are representing the same line.
Since the equations represent the same line, they have infinitely many solutions.
Therefore, the number of solutions for this system is infinitely many solutions.
Therefore, the correct answer is: infinitely many solutions.