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) About Me  (Show Source):
You can put this solution on YOUR website!
Same as system%285x-4y=1%2C5x-4y=1%29. What does that tell you? PARALLEL LINES. Are you looking for just the lines, or point of intersection?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The reason is that they are the same equation!
(1) +5x+-+4y+=+1+
(2) +10x+-+8y+=+2+
--------------------
If you multiply both sides of (1) by +2+,
then you get (2)
( you haven't changed (1) AT ALL, by doing that )
OR
If you divide both sides of (2) by +2+, 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) About Me  (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 = %285x-1%29%2F4.

    Then I take x = 0 and calculate y = %285x-1%29%2F4 = %285%2A0-1%29%2F4 = -1%2F4.

    Next, I take x = 1 and calculate y = %285x-1%29%2F4 = %285%2A1-1%29%2F4 = 4%2F4 = 1.

    And so on . . . 


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

    Because you even didn't try.