Question 1116560
.
solve by addition method.

4x+4y=3
2x-8y=-1
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<pre>
4x + 4y =  3     (1)
2x - 8y = -1     (2)


Multiply equation (1) by 2 (both sides).  Keep equation (2) as is. You get an <U>equivalent</U> system

8x + 8y =  6     (1')
2x - 8y = -1     (2')


Now add equations (1') and (2').  The terms "8y" will cancel each other, and you will get a single equation for the unique unknown x:

8x + 2x = 6 + (-1),   or

10x = 5.   It implies  x = {{{5/10}}} = {{{1/2}}} = 0.5.


Next substitute the found value of x into equation (1).  You will get

4*0.5 + 4y = 3  ====>  4y = 3 - 4*0.5 = 1  ====>  y = {{{1/4}}} = 0.25.


<U>Answer</U>.  x = 0.5,  y = 0.25.


<U>Check</U>.   4*0.5 + 4*0.25 = 3     ! Correct !

         2*0.5 - 8*0.25 = -1     ! Correct !
</pre>

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Notice that the standard and official name of this method is  "the Elimination method".


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On solving systems of linear equations in two unknowns see the lessons

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

&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 a linear system of two equations in two unknowns by the Elimination method</A> 

&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-using-det.lesson>Solution of a linear system of two equations in two unknowns using determinant</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Geom-interpret-of-the-lin-system-of-two-eqns-with-two-unknowns.lesson>Geometric interpretation of a linear system of two equations in two unknowns</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 lessons are 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.