What is the number of solutions and solution of 3x+2y=10 and 3x+2y=2 ??

Question

What is the number of solutions and solution of 3x+2y=10     and 3x+2y=2 ??

anonymous · Answer

@Mertsj help please?

anonymous · Answer

they are identical on the left side, but different on the right
what does that tell you?

anonymous · Answer

let us rewrite the equations in slope-intercept form.
what do we get as slopes for the two lines?

anonymous · Answer

@electrokid the slope is 2

anonymous · Answer

$y = mx+b$
re-arrange the equations like this.

anonymous · Answer

2y=3x+10 and 2y=3x+2

anonymous · Answer

yes.
then divide by "2"

anonymous · Answer

because we want "y" on its own

anonymous · Answer

let me show the first one
$$3x+2y=10\
-3x\quad-3x\
------\
2y=-3x+10\\text{divide by 2}\
{2y\over 2}={-3\over 2}x+{10\over 2}\
\boxed{y={-3\over2}x+5}
$$similarly, for the second one

anonymous · Answer

i got y=3/2+5 and y=3/2+1

anonymous · Answer

you missed the "x"  in them

anonymous · Answer

oh yeah my bad but i do know what you mean, and my next step would be what?

anonymous · Answer

what did you get for the second equation?

anonymous · Answer

and what do we get for the slopes of each line?

anonymous · Answer

well?

anonymous · Answer

i will butt in for a second, and then butt out
how is it possible for $3x+2y$ to equal two different numbers? 
it is not

anonymous · Answer

the slope is 3/2 for both

anonymous · Answer

-3/2 for both

and lines with equal slopes are parallel to each other.
since parallel lines never intersect, there are NO SOLUTIONS for the given equations

anonymous · Answer

kapeesh?

anonymous · Answer

kapeesh xD and my hw also asks for the solution though?

anonymous · Answer

ok i will but back in

if $3x+2y=10$  then it cannot also equal 2, and vice versa

anonymous · Answer

so, what will your answer be for that? 
@satellite73 that is logical. Teachers usually want the answer using the "textual" method :/

anonymous · Answer

idk i got 0

anonymous · Answer

@electrokid ^

anonymous · Answer

0 what?
0 number of solutions 
there are no solutions..

i.e., there is no such pair of (x,y) that will lie on both the lines since they are parallel
|dw:1367285559443:dw|

anonymous · Answer

so then why would my teacher put solutiion in my hw if there isnt any?

anonymous · Answer

to trick ya

anonymous · Answer

so im just suppose to put 0,0 on there @electrokid

anonymous · Answer

(0,0) is a point. so you cannot put that.
what is the number of solutions? __
what are the solutions? __ explain

anonymous · Answer

the solutions are 5 and 1

anonymous · Answer

@electrokid  is it right?