SOLUTION: 6x-y=-2 -18x+3y=4

Algebra ->  Algebra  -> Systems-of-equations -> SOLUTION: 6x-y=-2 -18x+3y=4      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 127287: 6x-y=-2
-18x+3y=4
Answer by jim_thompson5910(28717) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:

system%286x-y=-2%2C-18x%2B3y=4%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

6x-y=-2 Start with the first equation


-y=-2-6x Subtract 6x from both sides


-y=-6x-2 Rearrange the equation


y=%28-6x-2%29%2F%28-1%29 Divide both sides by -1


y=%28%28-6%29%2F%28-1%29%29x%2B%28-2%29%2F%28-1%29 Break up the fraction


y=6x%2B2 Reduce



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

Since y=6x%2B2, we can now replace each y in the second equation with 6x%2B2 to solve for x



-18x%2B3highlight%28%286x%2B2%29%29=4 Plug in y=6x%2B2 into the first equation. In other words, replace each y with 6x%2B2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



-18x%2B%283%29%286%29x%2B%283%29%282%29=4 Distribute 3 to 6x%2B2


-18x%2B18x%2B6=4 Multiply


6=4 Combine like terms on the left side


0=4-6Subtract 6 from both sides


0=-2 Combine like terms on the right side




Since this equation is never true for any x value, this means there are no solutions. So the system is inconsistent.