Daily PWN 003:

y= 3x+4

ax-by= 11 Find (b/a). The system has no solutions.

Is ax-by=11 in standard form of a line? If so, doesn’t the formula -(A/B) equal the slope? A has to positive, so A=3 and B= -1. So, -(3/-1)= 3… so B/A= -1/3. The actual answer is 1/3. Can you explain to me what I did wrong? Thanks!

(Link to the question.)

You’re losing a negative sign when you calculate the slope of the second equation. To see why, manipulate it a bit to get it into slope-intercept form:


When a linear system has no solutions, you know you’re dealing with parallel lines. Once you have both equations in slope-intercept form, it’s easy to see that \dfrac{a}{b} must equal 3 to make the lines parallel. If that’s true, then the reciprocal \dfrac{b}{a}=\dfrac{1}{3}.

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