Questions on Algebra: Systems of Linear Equations answered by real tutors!

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Question 169624: Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent:
2x-y=4
2x-y=3: Solve each system by substitution. Determine whether the equations are independent, dependent or inconsistent:
2x-y=4
2x-y=3
Answer by jim_thompson5910(9921) About Me  (Show Source):
You can put this solution on YOUR website!


Start with the given system of equations:

system(2x-y=4,2x-y=3)



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+4 Rearrange the equation


y=(-2x+4)/(-1) Divide both sides by -1


y=((-2)/(-1))x+(4)/(-1) 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((2x-4))=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+4=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