SOLUTION: I am having trouble with the following problem. I truly need help. 9x + 24y = 90 3x + 8y = 30 These need to be solved using the multiplication/addition method. I have seve

Algebra ->  Equations -> SOLUTION: I am having trouble with the following problem. I truly need help. 9x + 24y = 90 3x + 8y = 30 These need to be solved using the multiplication/addition method. I have seve      Log On


   

Question 199797: I am having trouble with the following problem. I truly need help.
9x + 24y = 90
3x + 8y = 30
These need to be solved using the multiplication/addition method. I have several more problems like this and will use this as an example. I need step by step directions so I can do the other problems. Thank-you so, so much!!!
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%289x%2B24y=90%2C3x%2B8y=30%29


-3%283x%2B8y%29=-3%2830%29 Multiply the both sides of the second equation by -3.


-9x-24y=-90 Distribute and multiply.


So we have the new system of equations:
system%289x%2B24y=90%2C-9x-24y=-90%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%289x%2B24y%29%2B%28-9x-24y%29=%2890%29%2B%28-90%29


%289x%2B-9x%29%2B%2824y%2B-24y%29=90%2B-90 Group like terms.


0x%2B0y=0 Combine like terms.


0=0Simplify.


Since 0=0 is always true, this means that there are an infinite number of solutions.

So the system is consistent and dependent.


If you have any questions, email me at jim_thompson5910@hotmail.com.
Check out my website if you are interested in tutoring.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I am having trouble with the following problem. I truly need help.
9x + 24y = 90
3x + 8y = 30
These need to be solved using the multiplication/addition method. I have several more problems like this and will use this as an example. I need step by step directions so I can do the other problems. Thank-you so, so much!!!
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That's the elimination method - you eliminate the variables by multiplying to get the same coefficient for one of them.
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For this example, tho, eqn 1 is 3 times eqn 2. No single solution is possible.
If you graph these 2, you get the same line twice.