The given equations are
6x - 12y = -24
3y = 2x + 18
We would solve for y in both equations
For 6x - 12y = -24,
12y = 6x + 24
Dividing both sides by 12, it becomes
12y/12 = 6x/12 + 24/12
y = x/2 + 2
For 3y = 2x + 18,
Dividing both sides by 3, it becomes
3y/3 = 2x/3 + 18/3
y = 2x/3 + 6
The equation of a line in the slope intercept form is
y = mx + c
where m is the slope
By comparing both equations, the slopes are different. They are not negative reciprocals of each other. Thus, they are not perpendicular or parallel. Thus, the lines intersect
