Answer:
In this case, the system of equations has no solution.
Explanation:
To determine how many solutions the system of equations has, you can examine the relative slopes of the two lines. The system is as follows:
12x - 15y = 18
4x - 5y = 6
You can simplify the equations by dividing both sides of each equation by their respective coefficients to put them in slope-intercept form (y = mx + b), where m represents the slope:
From equation (1):
12x - 15y = 18
-15y = -12x + 18
y = (4/5)x - 6/5
From equation (2):
4x - 5y = 6
-5y = -4x + 6
y = (4/5)x - 6/5
The two equations have the same slope (4/5), and their y-intercepts are also the same (-6/5). This means the two lines are parallel. When parallel lines have the same slope but different y-intercepts, they do not intersect, and there is no solution to the system of equations.
So, in this case, the system of equations has no solution.