```Question 252793
convert both equations to slope intercept form.

slope intercept form of linear equation is y = mx + b where m is the slope and b is the  y-intercept.

3x - 2y = 1 is the first equation.
subtract 3x from both sides to get:
-2y = -3x + 1
divide both sides of the equation by -2 to get:
y = (3/2)*x - (1/2)

slope for this equation is (3/2).

y - (2k + 1)*x = 3 is the second equation.
add (2k+1)*x to both sides to get:
y = (2k+1)*x + 3

slope for this equation is (2k+1)

if the lines are parallel, then their slopes are equal.

this means that:

2k+1 = (3/2)

subtract 1 from both sides of this equation to get:

2k = 1/2

divide both sides of this equation by 2 to get:

k = (1/4)

substitute this value for k in the second equation.

second equation is:

y - (2k + 1)*x = 3

substitute k = (1/4) in this equation to get:

y - (2*(1/4) + 1)*x = 3

simplify to get:

y - (3/2)*x = 3

add (3/2)*x to both sides of this equation to get:

y = (3/2)*x + 3

y = (3/2)*x - (1/2) (first equation)
y = (3/2)*x + 3 (second equation)

since they have the same slope, they are parallel to each other.

graph of these equations looks like this:

{{{graph(600,600,-10,10,-10,10,(3/2)*x - (1/2),(3/2)*x + 3)}}}

```