Question 465426: solve a system by elimination?
problem:
-3 + 6y = -9
5x - 6y = 19
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443)   (Show Source):
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
My first remark is that I don't believe that you rendered your first equation properly. I suspect that you meant:
Ordinarily the first step in an Elimination solution is to multiply one or the other (sometimes both) by a factor (or factors) so that you have one of the variables with coefficients in the two equations that are additive inverses.
In this problem, you can skip that step because the 6 on the  in the first equation is the additive inverse of the -6 on the in the second equation.
Add the two equations, term by term. The result will be (because of the additive inverse relationship of the coefficients on ) elimination of the variable and a single variable equation in  that you can solve by ordinary means.
Once you have solved for , you can substitute back into either of the original equations to derive a single variable equation in . After you have solved for , you can create an ordered pair ) from your calculated values that is the solution set of the system.
There are two possibilities that can occur that will cause you to fail to find a unique solution. (Neither of these possiblitities arise in the solution to the given problem, but you do need to be aware of the situation). First is when the result of adding the two equations is a triviality, such as  . In this case, you have a consistent dependent system meaning that the solution sets of both equations are identical, which is to say that their graphs would be the same line. Second is when the result is an absurdity such as  . In this case you have an inconsistent system meaning the intersection of the two solution sets is the null set, which is to say that their graphs would be distinct parallel lines.
John
My calculator said it, I believe it, that settles it
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