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## Topic review (newest first)

Ricky
2005-12-05 07:08:10

"1. If m+2=0;m=2
0x=-2
No solution"

Not true.  Let m = 2, then you get the equations: 2x + y = 2, so y = -2x + 2, and y = 2x + 4.  A common solution to these is the point (-1/2, 3).

"2. 2. If m+2≠0;m≠2
x=-2/(m+2)
So:
No solution-
m=2
One solution-
m≠2"

The logic here is right, if m = 2 had no solutions, than all lines without that slope intersect the line.  Unforutunately, m = 2 has a solution.

"Infinite many solutions-
m∈{}"

Correct.  The x-intercepts are off, and they only thing you can change is the slope.

krassi_holmz
2005-12-05 04:58:52

Sorry Ricky. But Sarah can still answer the question and can verify it with mine.

RickyOswaldIOW
2005-12-05 03:04:04

I wanted sarah to answer the question krassi

krassi_holmz
2005-12-05 02:42:05

y-2x=4 ⇒y=2x+4 ⇒
mx+y=2 <=>mx+2x+4=2
(m+2)x+4=2
(m+2)x=-2
1. If m+2=0;m=2
0x=-2
No solution
2. If m+2≠0;m≠2
x=-2/(m+2)
So:
No solution-
m=2
One solution-
m≠2
Infinite many solutions-
m∈{}
sorry for the syntax, I don't know English well.

RickyOswaldIOW
2005-12-05 02:17:24

What are the answers sarah? I don't.

sarah
2005-12-05 02:14:15

I get it, I get it! :-D

lol, thanks a lot:)

Ricky
2005-12-05 01:59:27

First, off the bat you should recognize mx+y=2 and y-2x=4 as equations of lines.  Now, remember (or learn), that the "solution" to these equations is that line.  That is, every (x, y) on that line will work out so that 0 = 0 when you plug it in.  1. When do two lines have no common solution?  In other words, when do two lines share no points?  2. When do two lines share all points?  And finally, 3. When do two lines share only one point?

sarah
2005-12-05 01:50:26

find the value(s) of m such that the equations mx+y=2, y-2x=4 have

1. No solution.

2. An infinite number of solutions.

3. One real solution.

I don't know how to solve these kinds of problems :s. please, help someone?

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