Question

Determine whether the lines are parallel, intersect, or coincide. 6x-4y=24, 3yy+2x=12

Answer 1

Parallel lines have the same slope.

Coincide lines have the same equation.

Intersect lines have different slope.

-------------------------------------------------------------

6x - 4y = 24, 3y + 2x = 12 - different equation (not coincide)

`6x-4y=24\qquad\text{subtract 6x from both sides}\\\\-4y=-6x+24\qquad\text{divide both sides by (-4)}\\\\y=(-6)/(-4)x+(24)/(-4)\\\\y=(3)/(2)x-6\to slope=(3)/(2)\\------------------------\\3y+2x=12\qquad\text{subtract 2x from both sides}\\\\3y=-2x+12\qquad\text{divide both sides by 3}\\\\y=(-2)/(3)x+(12)/(3)\\\\y=-(2)/(3)x+4\to slope=-(2)/(3)`

The lines have different slope, therefore are intersect.