SOLUTION: 3x+4y=15 -4x-3y=-20 I need to solve this through the addition method. Is there an easy way to do this?

Question 428131: 3x+4y=15
-4x-3y=-20
I need to solve this through the addition method. Is there an easy way to do this?
Found 2 solutions by htmentor, solver91311:
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
If, by addition method you mean adding one equation to the other, then proceed as follows:
3x + 4y = 15 (1)
-4x - 3y = -20 (2)
First multiply equation (1) by 4 and equation (2) by 3:
12x + 16y = 60
-12x - 9y = -60
Add the two equations:
7y = 0 -> y = 0
Substituting into equation (1) above, we get:
3x = 15 -> x = 5
So the solution is x = 5, y = 0
Below are the graphs of the two functions:

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

I cannot answer the question you asked. The problem is that "easy" is a relative term. What is easy for some is difficult for others, furthermore there are a number of specific ways to attack this problem for which the ease of accomplishment varies slightly. Below find what I consider to be the easiest method -- just how easy that is for you is something I am unable to guess.

In order to solve a system by the addition method, you must find a multiplier for one of the equations or a pair of multipliers, one for each of the equations such that the resulting coefficient on one of the variables in one of the equations is the additive inverse of the coefficient of that same variable in the other equation.

In your case, if you multiply the first equation by 3 and the second equation by 4, the coefficients on y end up being 12 and -12. Then when you add the two equations term by term, the coefficient on y in the result is zero, effectively eliminating the y variable and leaving you with a single equation in a single variable, in this case x.

By the way, because the goal of the method is to eliminate one of the variables, the Elimination Method is a more descriptive name than the Addition Method.

John

My calculator said it, I believe it, that settles it

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