Question 1111880
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<pre>
ax + by + c = 0     (1)
bx + ay + c = 0     (2)


Equivalently

ax + by = -c        (3)
bx + ay = -c        (4)


Multiply eq(3) by b (both sides).  Multiply eq(4) by a (both sides).  You will get


abx + b^2y = -bc    (5)
abx + a^2y = -ac    (6)


Subtract (5) from (6). In this way, you eliminate "x" :


(a^2 - b^2)y = -c*(a-b)  ====>  y =  {{{(-c*(a-b))/(a^2-b^2)}}} = {{{(-c*(a-b))/((a-b)*(a+b))}}} = // cancel (a-b) // = {{{(-c)/(a+b)}}}.


What I did is: I started from (3),(4) and eliminated x; in this way I got y.


Now  <U>YOU</U>  return to (3),(4);  eliminate y and get x.
</pre>

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You may find these lessons useful to you:

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&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 the linear system of two equations in two unknowns</A> 


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.