Question 1116568
.
solve by addition method.

8x-3y=18
4x+5y=-4
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<pre>
 8x - 3y =  18     (1)
 4x + 5y =  -4     (2)


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

 8x -  3y = 18     (1')
-8x - 10y =  8     (2')


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

-3y + (-10y) = 18 + 8,   or

-13y = 26.   It implies  y = {{{26/(-13)}}} = -2.


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

8x - 3*(-2) = 18  ====>  8x = 18 + 3*(-2) = 12  ====>  x = {{{12/8}}} = {{{3/2}}}.


<U>Answer</U>.  x = {{{3/2}}},  y = -2.


Check the answer on your own.
</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.