SOLUTION: Solve the linear systems using any method of your choice. 2x-y=1 4x-2y=2

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Question 1177923: Solve the linear systems using any method of your choice.
2x-y=1
4x-2y=2
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

2x-y=1
4x-2y=2.........both divide by 2
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2x-y=1
2x-y=1
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=> These two lines are exactly the same line. Therefore, the given system of equation has infinitely many solutions.

Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.

Consider the extended matrix. 


It is easy to see that its rows are proportional.



It means that one equation is equivalent to the other equation,

so FACTUALLY you have only one equation in two unknowns.



Such system has INFINITELY MANY solutions.


Take x as a FREE variable and express  y = 2x-1  from the first equation.


You may give any value to x and calculate the respective value of y: each such a pair (x,y) will be a solution.

Solved and explained.

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See the lesson
    - Geometric interpretation of the linear system of two equations in two unknowns
in this site.