SOLUTION: solve the system of equations by graphing, Identify if the system is inconsistent or dependent y=1/2x+2 y=2x-1

Algebra ->  Linear-equations -> SOLUTION: solve the system of equations by graphing, Identify if the system is inconsistent or dependent y=1/2x+2 y=2x-1      Log On


   

Question 243222: solve the system of equations by graphing, Identify if the system is inconsistent or dependent
y=1/2x+2
y=2x-1
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
The two equations are:
%0D%0Ay+=+%281%2F2%29x+%2B+2%0D%0A
%0D%0Ay+=+2x+-1%0D%0A
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We can express these by showing a graph with two straight lines defined by the given equations.
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%0D%0Agraph%28500%2C500%2C-10%2C10%2C-10%2C10%2C+1%2F2%2Ax+%2B+2%2C+2x-1%29%0D%0A
Using the graph we see that the two lines cross, so there is at least one point in common. That means there is at least one solution to the pair of equations, so they are CONSISTENT. If there were no points in common, they would be terms 'inconsistent'.
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We also see that there is ONLY one point in common. That means they are INDEPENDENT. To say they are dependent would mean that every point defined by one equation would define a point in the other one. This clearly is not the case.
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That's all the question asked. Going further could lead to trouble. But if you're adventurous.
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Since equals are equal, you could set the two equations define in 'y' to equal each other.
2x -1 = 1/2x + 2
Multiply by 2 to eliminate the fraction
4x - 2 = x + 4
Subtracting x from both sides
3x -2 = 4
Adding 2 to both sides
3x = 6
Dividing by 3
x= 2
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So, the solution to the system of equations is 2.
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But you could tell that was solution by simply looking at the graph.