Question

What is the correct classification of the system of equations below?

2x + 6y = 8
y - 2x = 2
a.parallel
b.coincident
c.intersecting

Answer 1

2x + 6y = 8 ---> 6y=-2x+8 ---> y= (-1/3) x + (4/3)
y - 2x = 2 ---> y=2x+2

so the system of equations that you really have (in slope intercept form) is...

y= (-1/3) x + (4/3)
y=2x+2


Choose the answer to each question.


All parallel lines ave the same slope.
IN YOUR SYSTEM, are their slopes the SAME? YES / NO




Coincident lines, are lines that are multiples of each other. For example if you had the following system, y = 2x + 4 (and)
3y = 6x + 12 you can see that the second equation is the same as the first one, if you divide everything in it by 3.
(coincident in English means IDENTICAL)

So is your system of equation like this, meaning; is it "coincident" ? YES / NO


Any lines that are not parallel, or any lines that are not the same they intersect, and therefore can be identified as "intersecting lines".
you can tell this in any system of equations by comparing their slopes (when the equations are in "slope intercept" form) .

In your system, are the slope the same? YES / NO
Do the lines intersect? YES / NO