How many solutions does the system of equations have? 9x − 12y = 24 and 3x = 4y
one
two
infinitely many
none
The given system of equations is:
9x − 12y = 24
3x = 4y
To find the number of solutions for this system, we can try to solve it using any of the methods such as substitution or elimination.
We can rearrange the second equation as:
3x - 4y = 0
Now, if we multiply the second equation by -3, we get:
-3(3x - 4y) = -3(0)
-9x + 12y = 0
We can see that this equation is the same as the first equation, meaning that the two equations represent the same line. Therefore, the two equations have infinitely many solutions.
The system of equations has infinitely many solutions.