SOLUTION: I can't find the points for the equations 5x-4y=1 and 10x-8y=2. Can you help me ?

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Question 1042186: I can't find the points for the equations 5x-4y=1 and 10x-8y=2. Can you help me ?
Found 3 solutions by josgarithmetic, josmiceli, ikleyn:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Same as . What does that tell you? PARALLEL LINES. Are you looking for just the lines, or point of intersection?
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
The reason is that they are the same equation!
(1)
(2)
--------------------
If you multiply both sides of (1) by ,
then you get (2)
( you haven't changed (1) AT ALL, by doing that )
OR
If you divide both sides of (2) by , then
you get (1)
( again, you haven't changed (2) the least bit )
--------------------------------------------
When you are comparing 2 linear equations like this,
the possibilities are:
(1) They are the same equation
(2) They are parallel equations
(3) They intersect at some point
-----------------------------
Hope this helps
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
I can't find the points for the equations 5x-4y=1 and 10x-8y=2. Can you help me ?
~~~~~~~~~~~~~~~~~ 

1.  These two equations are equivalent to one equation

    5x - 4y = 1.

    Therefore, they represent ONE STRAIGHT LINE.

    Or, one can say, that the two equations represent two straight lines that coincide.

    For details, see the lesson Geometric interpretation of a linear system of two equations in two unknowns in this site.


2.  Why you can't find the points for the equations?
    I can easily do it. I rewrite the first equation as 5x-1 = 4y and then as y = .

    Then I take x = 0 and calculate y =  =  = .

    Next, I take x = 1 and calculate y =  =  =  = 1.

    And so on . . . 


3.  Do you know why you coudn't do it? 

    Because you even didn't try.


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