MEDAL/FAN
If the slopes are
________
(the same, different) the system will have a solution. If the slopes are the same, then look at the y intercepts. If the y intercepts are the same, then there are
_______
(no solution, infinite solutions, one solution). If the slopes are the same, but the y intercepts are
_________
(the same, different), then there is no solution.

Question

MEDAL/FAN
If the slopes are
________
(the same, different) the system will have a solution. If the slopes are the same, then look at the y intercepts.  If the y intercepts are the same, then there are
_______
(no solution, infinite solutions, one solution).  If the slopes are the same, but the y intercepts are
_________
(the same, different), then there is no solution.

mathmale · Answer

Please share what YOU think the answers are, and defend your choices.  Then it'd be easier to give you some meaningful feedback.

anonymous · Answer

okay THE SAME because you can check your problem by plugging it in.

anonymous · Answer

@whpalmer4

anonymous · Answer

i think its 
1. the same
2. not sure
3. diffferent

mathmale · Answer

Thanks for sharing your own efforts.
I respectfully disagree with your response to #1.  Please think about this and defend your answer again, or change your answer and defend your new answer.

anonymous · Answer

okay sure

anonymous · Answer

well im going to go with different then because you can still plug it back in and i really don't know...

anonymous · Answer

@mathmale

anonymous · Answer

@whpalmer4

anonymous · Answer

I just need the second one @Owlcoffee

owlcoffee · Answer

Following Mathmales method, you'd have to re-meditate that answer see if the scenaro can be justified with it.
Now, if two lines have the same slope and their y-intersection is also the same, that must mean something, note that lines with same slope are parallel.

anonymous · Answer

Oh i think i'm starting to get it now.

mathmale · Answer

I think you should try drawing examples of lines with same slope and lines with different slopes.  The principles involved would become more obvious then.

anonymous · Answer

thank you.

mathmale · Answer

If you are given the equation of a line and then are told to multiply that entire equation by 2, how would the 2nd line relate to the first line?

whpalmer4 · Answer

Perhaps a picture would help.  

Let's take one of the typical coin problems.  You have a combination of 13 nickels and dimes in your pocket, and it adds up to 95 cents.  How many of each do you have?

Well, we can write two equations to represent this information. 

$$n+d = 13$$This just says we have 13 coins$$5n+10d=95$$This says the value of all of the nickels (5 cents each) plus the value of all of the dimes (10 cents each) is 95 cents.

I will plot both of these equations on the same graph (attached below).

whpalmer4 · Answer

Notice that the lines cross at a single point.  That means there is a single solution to this system of equations.  If you look at the axes, you can see that the solution is 6 dimes and 7 nickels, $6*10 + 7*5 = 95$

whpalmer4 · Answer

Two lines on the same plane which are not parallel will eventually intersect.  There is only one point in common to both lines, which is the point of intersection.  If the lines represent solutions to the equations they represent, then the point of intersection is the only solution which satisfies both equations

If we had two lines which were parallel, they would never intersect, and we would not have a solution.  There are no points in common.

If we have two lines which are coincident (read: exactly the same), then every point on the line, all infinity-zillion of them, is a solution to both equations, and we have infinitely many solutions.