To find the number of solutions the system has, we can check if the lines represented by the equations are parallel, intersecting, or coinciding.
We can rearrange the first equation to solve for y:
12x - 15y = 18
-15y = -12x + 18
y = (4/5)x - 6/5
Similarly, we can rearrange the second equation to solve for y:
4x - 5y = 6
-5y = -4x + 6
y = (4/5)x - 6/5
Both equations have the same slope of 4/5, which means their lines are parallel.
Parallel lines do not intersect, so the system has no solutions.
How many solutions does the system have? 12x−15y=18 4x−5y=6
1 answer