Determine a parameter in such a way that two lines are parallel

Question

The lines

$px + (2p-1)y + 4 = 0$

and

$(p+3)x + 2py + 6 = 0$

are parallel to each other. Find $p$.

I have no idea how to tackle this problem, can anyone help?

Answer 1

As the two lines are parallel to each other, so the coefficients should satisfy that $\frac{p}{p+3}=\frac{2p-1}{2p}$, or $2p^{2}=(p+3)(2p-1)$, so $p=\frac{3}{5}$.

Answer 2

Find the slopes of the two lines and equate them to each other and solve for $p$.

Answer 3

If two lines are parallel then their slopes are equal.Equate slopes of two lines and you get a quadratic equation.Solve it for your answer.

Answer 4

Two lines in 2-dimensions are parallel if and only if they have the same slope. So, just find the slope of both lines. If you write both in the form $y = mx + b$, then $m$ is the slope. So, for both, solve for $y$.

Answer 5

Fact that lines $px + (2p-1)y + 4 = 0$ and $(p+3)x + 2py + 6 = 0$ are parallel one with other means that corresponding system of two above equations has no solutions, then apply Cramer's rule.