{y=x+6
{y=1+x
BEST answer will be chosen!
2006-07-06 07:26:23 · 8 answers · asked by Brandon ツ 3 in Science & Mathematics ➔ Mathematics
I noticed another question you asked which utilized the addition method, so let's use that here and talk about possible results.
When you are using the addition method, you want to "line up" everything. Let's rewrite the equations so that the variables are on one side and the constants are on the other.
y = x + 6 becomes -x + y = 6
y = 1 + x becomes -x + y = 1
Now you want to multiply one or both of the equations so that the leading coefficients on one of the variables are additive inverses. To state that in English, you want to set it up so that one of the variables will disappear when the equations are added together.
Notice that if we multiply the first equation by (-1), then I will have a positive x in the first equation and a negative x in the second--this will cancel them out. So let's do that.
-x + y = 6 becomes x - y = -6
Now I have these equations.
x - y = -6
-x + y = 1
Add these together (add each column) and you get
0x + 0y = -5 which is the same as 0 = -5.
Now let's talk about possible outcomes for a moment. There are three things that can happen when you add the equations in this method. The first is that you cancel one variable but the other is still there. This gives you something to use to find a solution, so there is a unique solution to the problem--the system of equations in independent.
The second alternative is that both of the variables disappear and you have a true statement, like 0 = 0. If this happens, then they gave you two equations which are identical, so the system of equations is dependent. You have two equations of the same line.
The other alternative is that both of the variables disappear and you have a false statement. That is what happened here, because you ended up with 0 = -5 (which is false). This means that they gave you equations for two lines which are parallel. The fact that the resulting statement is false means that the lines never intersect. So the system is inconsistent.
That is how to "read the results" when you are working with the addition method.
2006-07-06 14:13:43 · answer #1 · answered by tdw 4 · 5⤊ 1⤋
Systems of equations with no solution are called inconsistent. Sor for a system of two linear equations, this means that their graphs are parallel lines and do not intersect. But we knew this, right?? The slopes are the same. Try setting the two equations equal to each other. You'll get some absurdity like 5 = 0. That should help you.
2006-07-06 08:53:00 · answer #2 · answered by Ervin C 1 · 0⤊ 0⤋
This system is inconsistent because if you graph the lines, they will be parallel. You can tell that they will be parallel because they have the same slope (1), but different y-intercepts (1 and 6).
2006-07-06 07:32:08 · answer #3 · answered by mathsmart 4 · 0⤊ 0⤋
Inconsistent....if you set 1+x=x+6 you get 1=6 which is not true....
2006-07-06 07:30:57 · answer #4 · answered by jenn 4 · 0⤊ 0⤋
from y=x+6
to:
y=1+x
The difference will always be 5. Inconsistent.
2006-07-06 07:37:26 · answer #5 · answered by Milo 3 · 0⤊ 0⤋
they are inconsistent, since both problems have the same slope and different y-intercepts
2006-07-06 14:40:34 · answer #6 · answered by Sherman81 6 · 0⤊ 0⤋
inconsistent
2006-07-06 09:17:01 · answer #7 · answered by Olivia 4 · 0⤊ 0⤋
idk...it's summer i don't feel like doin math
2006-07-06 07:29:48 · answer #8 · answered by Darling 4 · 0⤊ 0⤋