Question

tell whether the system has one solution, infinitely many solutions, or no solutions.

6y=-5x+24
2.5x+3y=12

Answer 1

To determine whether the system has one solution, infinitely many solutions, or no solutions, we can solve the system of equations.

First, let's rearrange the equations to be in slope-intercept form (y = mx + b):

6y = -5x + 24 ==> y = (-5/6)x + 4

2.5x + 3y = 12 ==> 3y = -2.5x + 12 ==> y = (-2.5/3)x + 4

Comparing the two equations, we can see that they have the same slope (m = -5/6 = -2.5/3), but different y-intercepts (b = 4 ≠ 12).

Since the slopes are the same, but the y-intercepts differ, the lines are parallel and will never intersect. Therefore, the system has no solutions.