SOLUTION: When solving a system of equations, how do I know what numbers to put in place of x and y? An example is: 2x – 6y = 42 3x – 9y = -15 I am to solve similar systems of equat

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Question 147216: When solving a system of equations, how do I know what numbers to put in place of x and y? An example is:

2x – 6y = 42
3x – 9y = -15
I am to solve similar systems of equations but I do not understand what nubers to replace the variables with.
Can you help?
Thank you very much.
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%282x-6y=42%2C3x-9y=-15%29


-3%282x-6y%29=-3%2842%29 Multiply the both sides of the first equation by -3.


-6x%2B18y=-126 Distribute and multiply.


2%283x-9y%29=2%28-15%29 Multiply the both sides of the second equation by 2.


6x-18y=-30 Distribute and multiply.


So we have the new system of equations:
system%28-6x%2B18y=-126%2C6x-18y=-30%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:


%28-6x%2B18y%29%2B%286x-18y%29=%28-126%29%2B%28-30%29


%28-6x%2B6x%29%2B%2818y%2B-18y%29=-126%2B-30 Group like terms.


0x%2B0y=-156 Combine like terms. Notice how the x terms cancel out.


0=-156Simplify.


Since 0=-156 is never true, this means that there are no solutions. So the two equations are inconsistent.