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Explain how and after how many steps you recognize a system of linear equation has no solution.

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1 Answer

It really depends on how complex the problem is as to how many steps it will take.  Eventually you will simplify the problem down to something like this:

3x-9 = 3x+4  so -9 = 4  ???

If you get that result that means that there is no possible solution since no value you substitute for x will make the statement true.

You may also get something that simplifies down to this:

3x + 4 = 3x +4  so 4 = 4

If you get this result it means you have infinite solutions since any value you substitute for x will make the statement true.

 

Hope this helps for the problem you are working on