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

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Question 177967: 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!
Solved by pluggable solver: Solving a linear system of equations by subsitution


Lets start with the given system of linear equations




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

Solve for y for the first equation

Subtract from both sides

Divide both sides by -1.


Which breaks down and reduces to



Now we've fully isolated y

Since y equals we can substitute the expression into y of the 2nd equation. This will eliminate y so we can solve for x.


Replace y with . Since this eliminates y, we can now solve for x.

Distribute -1 to

Multiply



Reduce any fractions

Subtract from both sides


Combine the terms on the right side



Now combine the terms on the left side.
Since this expression is not true, we have an inconsistency.


So there are no solutions. The simple reason is the 2 equations represent 2 parallel lines that will never intersect. Since no intersections occur, no solutions exist.


graph of (red) and (green) (hint: you may have to solve for y to graph these)


and we can see that the two equations are parallel and will never intersect. So this system is inconsistent
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