Question 1190535
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I'm having a really hard time understanding solving using elimination. Could somebody explain it to me in lots of detail.
x-y=3 and 2x+4y=9
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            Specially for the given problem,  the procedure  (the  Elimination method)  works as follows.



<pre>
Your starting system is

     x -  y = 3     (1)

    2x + 4y = 9     (2)


Now multiply first equation by 2 (both sides). Keep the second equation as is. You will get

    2x - 2y = 6     (3)

    2x + 4y = 9     (4)


Next, subtract equation (3) from equation (4). 

The terms "2x" in both equations will cancel each other, and you will obtain an equation for one single unknown "y":

    4y - (-2y) = 9 - 6,

or

       6y      =   3

        y      =   3/6 = 0.5.


So, one unknown is just found: y = 0.5.

To find another unknown "x", substitute the found value y= 0.5 into EITHER equation (1) or (2),

For example, substituting into equation (1) gives you

    x = 3 + y = 3 + 0.5 = 3.5.


At this point, the problem is just solved, and the answer is  x= 3.5,  y= 0.5.


You may check (and you MUST check) the answer by substituting the found values into the original / (given) equations.

I leave this job to you, since it is elementary.
</pre>


At this point, &nbsp;the solution is complete.


The idea of the method is to make the coefficients &nbsp;EQUAL &nbsp;in two equations for some 
of the two unknowns, &nbsp;and then subtract equations, &nbsp;ELIMINATING &nbsp;this unknown.


Having this explained solution, &nbsp;please &nbsp;NEVER &nbsp;say again that you do not understand the subject: 
it was explained to you in the most comprehensive and detailed way.



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To see many other similar solved problems, &nbsp;look into the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF= http://www.algebra.com/algebra/homework/coordinate/lessons/Solution-of-the-lin-syst-of-two-eqns-with-two-unknowns-Elimination-method.lesson>Solution of the linear system of two equations in two unknowns by the Elimination method</A> 

in this site.



Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


The referred lesson is the part of this online textbook under the topic "<U>Systems of two linear equations in two unknowns</U>".



Save the link to this online textbook together with its description


Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson


to your archive and use it when it is needed.