SOLUTION: Use linear combinations to solve the system of linear equations. 3b+2c=46 5c+b=11

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Question 176235: Use linear combinations to solve the system of linear equations.
3b+2c=46
5c+b=11
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5c%2Bb=11 Start with the second equation.


b%2B5c=11 Rearrange the terms.




Start with the given system of equations:
system%283b%2B2c=46%2Cb%2B5c=11%29


-3%28b%2B5c%29=-3%2811%29 Multiply the both sides of the second equation by -3.


-3b-15c=-33 Distribute and multiply.


So we have the new system of equations:
system%283b%2B2c=46%2C-3b-15c=-33%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:


%283b%2B2c%29%2B%28-3b-15c%29=%2846%29%2B%28-33%29


%283b%2B-3b%29%2B%282c%2B-15c%29=46%2B-33 Group like terms.


0b%2B-13c=13 Combine like terms.


-13c=13 Simplify.


c=%2813%29%2F%28-13%29 Divide both sides by -13 to isolate c.


c=-1 Reduce.


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3b%2B2c=46 Now go back to the first equation.


3b%2B2%28-1%29=46 Plug in c=-1.


3b-2=46 Multiply.


3b=46%2B2 Add 2 to both sides.


3b=48 Combine like terms on the right side.


b=%2848%29%2F%283%29 Divide both sides by 3 to isolate b.


b=16 Reduce.


So our answer is b=16 and c=-1.


This means that the system is consistent and independent.