SOLUTION: Show that the lines ax + by = c and dx + ey = f are parallel whenever ae − bd = 0

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Question 1197261: Show that the lines ax + by = c and dx + ey = f are parallel whenever ae − bd = 0
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Slopes should be equal.
That is, -a%2Fb=-d%2Fe
a%2Fb=d%2Fe
ae=bd
ae-bd=bd-bd
ae-bd=0

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YOU WERE GIVEN TWO equations all in variables only and also are given condition that the two linear equations are for PARALLEL LINES. That means, their slopes must be equal. Use the variable available in the two given equations. Maybe one might start with the "whenever" condition and work backward, but I did this in the other direction. IF the two lines parallel,.... then "ae-bd=0".

If you expected some graphing, then no do. You were not given two specific linear equations; you were given two linear equations in general. This is a symbolism exercise.