SOLUTION: -x+3y=4
x-3y=3
what is the elimination method to solve these two problems
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Question 662513: -x+3y=4
x-3y=3
what is the elimination method to solve these two problems
Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
-x+3y=4
x-3y=3
what is the elimination method to solve these two problems
-------------
It's 2 equations, 1 problem.
==============================
-x+3y=4
x -3y=3
--------- Add
0 + 0 = 7
--> inconsistent, no solution.
If you graph them, you get parallel lines.
No intersection, no solution.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
It is not two problems. It is two equations each of which is in two variables that together form one 2X2 system of linear equations.
Elimination Method.
1. Multiply one or both equations by a constant or constants such that the coefficient on one of the variables is the additive inverse of the coefficient on the same variable in the other equation. (For this system, you can skip this step since the coefficients on 
are already 1 and -1 and the coefficients on 
are already 3 and -3)
2. Add the two equations term by term. One (at least) of the variables will be eliminated leaving you either with a single equation in a single variable, a triviality (such as 0 = 0), or an absurdity (such as 0 = 4).
3. If a single equation in a single variable remains, solve it. Use the value you discover for that variable to substitute back into either of the original equations. That gives you a new single equation in the eliminated variable which you must now solve. The two values for the two variables form an ordered pair that is the solution set of the 2X2 system. Graphically, this is represented by two distinct lines that intersect in a single point.
4. If you end up with a triviality, then the solution set of the system is the solution set of either (and therefore both) of the two equations. Graphically, this is represented by each of the equations graphing to the same line.
5. If you end up with an absurdity, then the solution set of the system is the empty set. Graphically, this is represented by two parallel lines.
John
My calculator said it, I believe it, that settles it
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