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- anonymous

Elimination method
, how do I begin
2x-3y=-1
-4x+6y=2

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- anonymous

Elimination method
, how do I begin
2x-3y=-1
-4x+6y=2

- chestercat

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- jdoe0001

begin by well.... eliminating :)
\(\large \begin{array}{rrrrrllll}
2x-3y=-1&{\color{brown}{ \times 2}}\implies &\cancel{4x}-6y=-2\\
-4x+6y=2&\implies &\cancel{-4x}+6y=2
\\\hline\\
&&0+0=0
\end{array}\)

- jdoe0001

wel... to be fair \(\large \begin{array}{rrrrrllll}
2x-3y=-1&{\color{brown}{ \times 2}}\implies &\cancel{4x}\cancel{-6y}=\cancel{-2}\\
-4x+6y=2&\implies &\cancel{-4x}\cancel{+6y}=\cancel{2}
\\\hline\\
&&0+0=0
\end{array}\)

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- anonymous

I think I get confused on the beginning part in figuring out what number am I actually multiplying the equation by.

- jdoe0001

that simply means,, the lines are equal
if you notice the 2nd equation, is really the 1st one "times 2"
so the graph is just one line on top of the other

- jdoe0001

well.... first off, you'd want to put the "x" and "y"s all lined up vertically
all "x"s in the same column and all "y"s in the same column

- jdoe0001

then you take a peek of say, you want to eliminate the "x"
you take a peek at the "x" column
"what number can I multiply the top to make it equal to the bottom"?
or the "bottom to make equal to the top"
BUT negative

- anonymous

It's asking what is the solution of the system.

- jdoe0001

a solution occurs, when
there's an "x" value(s) and "y" value(s)
in graph wise, when the graphs meet or touch|dw:1438475183823:dw|

- jdoe0001

in this case, what you have is, on line on top of the other
so the lines are TOUCHING each other all over, from beginning to end
kinda like pancaking one line on top of the other
thus, there's no ONE solution, there's INFINITE solutions

- anonymous

ugh I am really trying to grasp the concept of elimination, but when I think I am close to understanding it ANOTHER method pops up !

- jdoe0001

for the algebraic part
elimination means, getting rid of one of the variables
for example
3x + 5y = 2
27x + 2y = 7
so you look at the top first, to cancel say the "x"
"can I multiply the 3x for "something" to make it 27x?"
well, 3x * 9 = 27x
so low and behold, we can, BUT, let's make it negative 27x
thus we'd use -9 instead
3x + 5y = 2 * -9 -27x - 45y = -18
27x + 2y = 7 27x + 2y = 7
notice, the -27x and the 27x below, cancel or "eliminate" each other

- jdoe0001

you add them vertically
the "x" variable gets eliminated
the "y" variable remains
then you solve for "y"
once you get "y", you can use that value on either equation to get "x"

- jdoe0001

or the other way around, you eliminate "y' to get "x"
either variable to get the other

- jdoe0001

anyhow, my dashing time :)

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