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

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

Multiply the both sides of the second equation by -3.

Distribute and multiply.

So we have the new system of equations:

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

Group like terms.

Combine like terms.

Simplify.

Since 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) (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!!!
-------------------
That's the elimination method - you eliminate the variables by multiplying to get the same coefficient for one of them.
------------
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.

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