How many solutions does the system have?%0D%0A12x−15y=18%0D%0A4x−5y=6(1 point)%0D%0AResponses

Answer 1

To determine the number of solutions, we can compare the slopes of the two equations:

The first equation is 12x - 15y = 18, which can be written as -15y = -12x + 18. Dividing both sides by -15, we get y = 4/5x - 6/5. Therefore, the slope of the first equation is 4/5.

The second equation is 4x - 5y = 6, which can be written as -5y = -4x + 6. Dividing both sides by -5, we get y = 4/5x - 6/5. Therefore, the slope of the second equation is also 4/5.

Since the slopes of the two equations are equal, the two lines are parallel and will not intersect. Therefore, the system has no solutions.