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

1. welshfella

Hint: multiply the first equation by 3 what do you get?

2. anonymous

-6+y=7?

3. 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)

4. 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 ?

5. 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?

6. anonymous

i got that the equations are parallel

7. 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

8. anonymous

thank you