How many solutions does the system of equations have?
9x − 12y = 24 and 3x = 4y
The two equations form a system of linear equations with two variables, x and y.
To determine the number of solutions, we can check if the two equations are consistent or inconsistent.
We can rewrite the second equation as 3x - 4y = 0.
Now, we have the following system of equations:
9x - 12y = 24
3x - 4y = 0
To check the consistency, we can divide the first equation by 3 and the second equation by -1:
3x - 4y = 8
3x - 4y = 0
Comparing the two equations, we can see that the left sides are the same, but the right sides are different. Therefore, the system of equations is inconsistent.
Since the system is inconsistent, it does not have any solutions.