Question 183235


Start with the given system of equations:

{{{system(4c+3d=-2,8c-2d=12)}}}



{{{-2(4c+3d)=-2(-2)}}} 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(-8c-6d=4,8c-2d=12)}}}



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



{{{(-8c-6d)+(8c-2d)=(4)+(12)}}}



{{{(-8c+8c)+(-6d+-2d)=4+12}}} Group like terms.



{{{0c+-8d=16}}} Combine like terms.



{{{-8d=16}}} Simplify.



{{{d=(16)/(-8)}}} Divide both sides by {{{-8}}} to isolate {{{d}}}.



{{{d=-2}}} Reduce.



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



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



{{{-8c-6(-2)=4}}} Plug in {{{d=-2}}}.



{{{-8c+12=4}}} Multiply.



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



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



{{{c=(-8)/(-8)}}} 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.