Question 1154176
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<pre>

    x - y = 0      (1)

    x + y = 16     (2)


This system can be solved in two ways.



1.  First method to use is the ELIMINATION method.

    Add equations 1) and (2)  (both sides).

    You will get


    2x = 16;  hence,  x = 16/2 = 8.


    Next, substitute the found value x= 8 into equation (1) to find "y".  You will get

    8 - y = 0,  which implies y = 8.


    <U>ANSWER</U>.  The solution to the system is  x= 8,  y= 8.




2.  The second method to use is the SUBSTITUTION method.


    From equation (1), express x = y.   Substitute it into equation (2), replacing "y" there.  You will get


    x + x = 16,   or  2x = 16,  which implies  x = 16/2 = 8.


    Then again, you substitute the found value of x= 8 into equation (1)  (same as you do in the solution ABOVE),

    and you get y = 8.


    <U>ANSWER</U>.  The solution to the system is  x= 8,  y= 8.
</pre>


The given system is one of simplest systems of two equations in two unknowns.


Actually, &nbsp;there are &nbsp;OTHER &nbsp;methods to use, &nbsp;beyond these two; &nbsp;for example the &nbsp;DETERMINANT &nbsp;method,

sometimes also called &nbsp;"the &nbsp;Cramer's rule".


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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.