## anonymous one year ago Elimination method , how do I begin 2x-3y=-1 -4x+6y=2

1. anonymous

@jamesr @RosieF @Chumpian

2. anonymous

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

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. anonymous

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|

10. anonymous

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

11. 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 !

12. anonymous

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

13. anonymous

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"

14. anonymous

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

15. anonymous

anyhow, my dashing time :)