SOLUTION: Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent: 2x-y=4 2x-y=3

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent: 2x-y=4 2x-y=3      Log On


   

Question 169624: Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent:
2x-y=4
2x-y=3
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%282x-y=4%2C2x-y=3%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

2x-y=4 Start with the first equation


-y=4-2x Subtract 2x from both sides


-y=-2x%2B4 Rearrange the equation


y=%28-2x%2B4%29%2F%28-1%29 Divide both sides by -1


y=%28%28-2%29%2F%28-1%29%29x%2B%284%29%2F%28-1%29 Break up the fraction


y=2x-4 Reduce



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

Since y=2x-4, we can now replace each y in the second equation with 2x-4 to solve for x



2x-highlight%28%282x-4%29%29=3 Plug in y=2x-4 into the second equation. In other words, replace each y with 2x-4. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



2x-2x%2B4=3 Distribute the negative


4=3 Combine like terms on the left side


0=3-4Subtract 4 from both sides


0=-1 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