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Elimination method
- Thread starter mnkrebs
- Start date
mnkrebs said:I am trying to solve using the elimination method
7r-3s=35
3r+7s=73
Do I multiply the first equation by 3 and the second equation by 7? I am using these numbers based on the fact that 21 is the lowest multiplier of 3 and 7.
You certainly COULD multiply the first equation by 3 and the second equation by 7:
3*(7r - 3s) = 3*35
7*(3r + 7s) = 7*73
The resulting equations would be these:
21r - 9s = 105
21r + 49s = 511
Do you see that you would need to SUBTRACT one equation from the other in order to eliminate the "r" terms (because 21r - 21r = 0r)
I'd suggest it might be easier to note that the "s" terms in the original problem already have opposite signs. If we could make the coefficients of "s" into opposites, then we could just add the equations together and eliminate the "s" terms. Since most people make fewer mistakes with adding equations together than they do when they're subtracting equations, this might be a better approach.
We could multiply the first equation by 7, and the second by 3:
7*(7r - 3s) = 7*35
3(3r + 7s) = 3*73
Here are the new equations:
49r - 21s = 245
9r + 21s = 219
Now, simply adding the two equations together will eliminate the "s" terms:
49r - 21s = 245
9r + 21s = 219
-----------------
58r + 0s = 464
or,
58r = 464
You should easily be able to find the value of "r". Once you have the value for "r", substitute it into one of the original equations and solve for "s".
Your way will work, too, of course....as long as you don't make an error when subtracting.
mnkrebs said:I probably should be able to easily find the value of r, but I don't know where to begin. I am really struggling with the entire concept. How do I find the value of r?
If you read my previous response carefully, you'll note that just BEFORE I said "you should be able to easily find the value of r," I gave you this equation:
58r = 464
To solve for r (which means to get r by itself on one side of the equation,) divide both sides by 58....
(58r)/58 = 464/58
If you cannot solve that equation, then you are probably not ready to attempt solving a system of equations with two variables. I suggest that you have a serious talk with your teacher, and perhaps consider hiring a tutor who can sit down "face-to-face" with you and help you get caught up with where you need to be to continue your studies.
We are happy to help you with specific problems you're having, but cannot re-create weeks of missing instruction.