what is the correct classification of this system of equations? -2x+y=7 3y=6x+4 answer choices are: parallel coincident intersecting

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what is the correct classification of this system of equations? -2x+y=7 3y=6x+4 answer choices are: parallel coincident intersecting

Mathematics
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Hint: multiply the first equation by 3 what do you get?
-6+y=7?
  • phi
I would rewrite both equations so that they are in the form y = mx + b and look at "m" (the number in front of the x) that is the slope. if the slopes are different , the lines will intersect if the slopes are the same, the lines are parallel (unless both equations are identical, in which case it's the same line for both equations)

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Other answers:

  • phi
First equation: -2x+y=7 add +2x to both sides -2x + 2x + y= 2x+7 or y= 2x + 7 what is the slope of this line ?
  • phi
second equation 3y=6x+4 divide both sides by 3 \[ \frac{3y}{3} = \frac{6x+4}{3} \\ y = \frac{6}{3} x + \frac{4}{3} \\ y= 2x + \frac{4}{3} \] what is the slope of this line?
i got that the equations are parallel
  • phi
yes, both equations have a slope of 2 but the equations are different, so the lines are parallel if the equation were the same, then the lines are "coincident" which is a fancy way to say they lie on top of each other... i.e. they are the same line
thank you

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