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

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) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

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

Start with the first equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

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

Since , we can now replace each in the second equation with to solve for

Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute the negative

Combine like terms on the left side

Subtract 4 from both sides

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

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