SOLUTION: 2x - y = 4 2x - y = 6 there is also a graph with this. help

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Question 103695: 2x - y = 4
2x - y = 6
there is also a graph with this. help
Answer by jim_thompson5910(35256) About Me  (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

2%2Ax-1%2Ay=4
2%2Ax-1%2Ay=6

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

-1%2Ay=4-2%2AxSubtract 2%2Ax from both sides

y=%284-2%2Ax%29%2F-1 Divide both sides by -1.


Which breaks down and reduces to



y=-4%2B2%2Ax Now we've fully isolated y

Since y equals -4%2B2%2Ax we can substitute the expression -4%2B2%2Ax into y of the 2nd equation. This will eliminate y so we can solve for x.


2%2Ax%2B-1%2Ahighlight%28%28-4%2B2%2Ax%29%29=6 Replace y with -4%2B2%2Ax. Since this eliminates y, we can now solve for x.

2%2Ax-1%2A%28-4%29-1%282%29x=6 Distribute -1 to -4%2B2%2Ax

2%2Ax%2B4-2%2Ax=6 Multiply



2%2Ax%2B4-2%2Ax=6 Reduce any fractions

2%2Ax-2%2Ax=6-4 Subtract 4 from both sides


2%2Ax-2%2Ax=2 Combine the terms on the right side



0%2Ax=2 Now combine the terms on the left side.
0%2F1=2%2F1 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 2%2Ax-1%2Ay=4 (red) and 2%2Ax-1%2Ay=6 (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