Question 452154: I need to solve this using the elimination method.
x + 5y=34
-x +9y = 50
The answer must be an ordered pair.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
Step 1 of the elimination method is to find a multiplier for one or the other of the equations such that the coefficients on one of the variables become additive inverses. Sometimes you have to find a multiplier for each of the equations.
For your situation, you can either skip step 1 because the coefficients on the x variable are already additive inverses, i.e. 1 and -1. Or, if you would rather, you can multiply the first equation by 9 and the second one by -5 so that the coefficients on the y variable become 45 and -45.
Whichever you decide, the second step is the same. You add the two equations term-by-term to get a single equation. Having used the multipier(s) as discussed causes one of the variables to be eliminated (hence the name "Elimination Method") leaving you with a single equation in a single variable that can be solved by ordinary means, which is to say by adding the same thing to both sides or multiplying both sides by the same thing until the variable is isolated on the left and you have a constant on the right.
Once you have solved the single variable linear equation for the variable that remains after the elimination step, you can take that value and substitute it back into either of the original equations and then solve the result for the other variable.
Finally, once you have determined the value of both variables, arrange them into an ordered pair (x, y). This is called an ordered pair because it is always in the order x first, y second.
John
My calculator said it, I believe it, that settles it
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