Question 1084079
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<pre>
1.  Finding x.  

    You have these two equations

    x = 3*r,   (1)   where "r" is unknown common ratio

    12 = x*r.  (2)


    Substitute (1) into (2). You will get  12 = (3*r)*r   or   12 ={{{ 3*r^2}}}.

    It implies {{{r^2}}} = {{{12/3}}} = 4.   Hence, r = 2 or -2.

    
    It gives two solutions for x:  x = 3*2 = 6   and    x = 3*(-2) = -6.



2.  Finding y.

    You just found that there are two possibilities for the common ratio: r = 2  and  r = -2.

    At the first possibility,  y = 12^2 = 24.

    At the second possibility,  y = 12*(-2) = -24.
</pre>

<U>Answer</U>. There are two solutions:  (x,y): = (6,24)  and  (x,y) = (-6,-24).


Solved.



On geometric progressions, read the introductory lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Geometric-progressions.lesson>Geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-geometric-progressions.lesson>The proofs of the formulas for geometric progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-geometric-progressions.lesson>Problems on geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-geometric-progressions.lesson>Word problems on geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problems-on-geometric-progressions.lesson>Solved problems on geometric progressions</A>



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

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


The referred lessons are the part of this online textbook under the topic <U>"Geometric progressions"</U>.