Question

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

Answer 1

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

Answer 2

-6+y=7?

Answer 3

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)

Answer 4

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 ?

Answer 5

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?

Answer 6

i got that the equations are parallel

Answer 7

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

Answer 8

thank you