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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?

5 Answers 5

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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.

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    I don't believe that we've reached that level of mathematics yet..2012-10-04
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Find the slopes of the two lines and equate them to each other and solve for $p$.

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    @ZafarS: If you don't already know that, then apply some independent thought. Can you find the axis intercepts with the equation of a line in this form? Can you find the slope of the line that connects those two intercept points?2012-10-04
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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.

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    I don't know how to get the slope of these lines, I am only familiar to the simple $ y =ax+b $2012-10-04
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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 $y$.

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    How do I do this? Can you give an example? I don't $k$now how to write these in the for$m$ y=ax+b..2012-10-04
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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 $p=\frac{3}{5}$.

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    Thank you, kind sir, I now understand.2012-10-07