SOLUTION: 4c+3d=-2 8c-2d=12

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: 4c+3d=-2 8c-2d=12      Log On


   

Question 183235: 4c+3d=-2
8c-2d=12
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%284c%2B3d=-2%2C8c-2d=12%29


-2%284c%2B3d%29=-2%28-2%29 Multiply the both sides of the first equation by -2.


-8c-6d=4 Distribute and multiply.


So we have the new system of equations:
system%28-8c-6d=4%2C8c-2d=12%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:


%28-8c-6d%29%2B%288c-2d%29=%284%29%2B%2812%29


%28-8c%2B8c%29%2B%28-6d%2B-2d%29=4%2B12 Group like terms.


0c%2B-8d=16 Combine like terms.


-8d=16 Simplify.


d=%2816%29%2F%28-8%29 Divide both sides by -8 to isolate d.


d=-2 Reduce.


------------------------------------------------------------------


-8c-6d=4 Now go back to the first equation.


-8c-6%28-2%29=4 Plug in d=-2.


-8c%2B12=4 Multiply.


-8c=4-12 Subtract 12 from both sides.


-8c=-8 Combine like terms on the right side.


c=%28-8%29%2F%28-8%29 Divide both sides by -8 to isolate c.


c=1 Reduce.


So our answers are c=1 and d=-2.


This means that the system is consistent and independent.