Question 1143890
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Unfortunately, the post is written and submitted by a person, who does not understand the meaning of the words he uses.



<U>Explanation</U>


<pre>
(1)  If TWO separate equations are presented in the post, then wording must be <U>THIS</U> :

         Solve equations  3x = 1(mod 7) and 5x = 1(mod 8)


     using <U>plural</U>  "equations".



(2)  If one entity is assumed, then wording must be <U>THIS</U> :

         Solve the system of two equations  3x = 1(mod 7) and 5x = 1(mod 8)


     using the term "system".
</pre>


I will assume the formulation #2.



<U>Solution</U>


<pre>
First equation,   3x = 1(mod 7),  is equivalent to  x = 5(mod 7).


Second equation,  5x = 1(mod 8),  is equivalent to  x = 5(mod 8).


Then the system is equivalent to one equation  x = 5(mod 56).


<U>ANSWER</U>.  The solution to the system is  x = 5(mod 56).
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