SOLUTION: I have to determine the number of solutions and identify the type of system, as well as checking my work. I am not sure how to check my work. Can someone help me? -6x+2y=4 3x-y=

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: I have to determine the number of solutions and identify the type of system, as well as checking my work. I am not sure how to check my work. Can someone help me? -6x+2y=4 3x-y=      Log On


   

Question 125998: I have to determine the number of solutions and identify the type of system, as well as checking my work. I am not sure how to check my work. Can someone help me?
-6x+2y=4
3x-y=-4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's solve this system by using substitution
Start with the given system of equations:

system%28-6x%2B2y=4%2C3x-y=-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%2B2y=4 Start with the first equation


2y=4%2B6x Add 6x to both sides


2y=%2B6x%2B4 Rearrange the equation


y=%28%2B6x%2B4%29%2F%282%29 Divide both sides by 2


y=%28%28%2B6%29%2F%282%29%29x%2B%284%29%2F%282%29 Break up the fraction


y=3x%2B2 Reduce



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

Since y=3x%2B2, we can now replace each y in the second equation with 3x%2B2 to solve for x



3x-highlight%28%283x%2B2%29%29=-4 Plug in y=3x%2B2 into the first equation. In other words, replace each y with 3x%2B2. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



3x-3x-2=-4 Distribute the negative


-2=-4 Combine like terms on the left side


0=-4%2B2Add 2 to 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 this also means that the system is inconsistent.