Question 1196577
.
<pre>
You want to solve a system of two equations in two unknowns

    3x + 5y = 54      (1)
    6x + 4y = 72      (2)


Divide second equation by 2 (both sides).  Keep equation (1) as is.
You will get

    3x + 5y = 54      (1)
    3x + 2y = 36      (2')


Now subtract equarion (2') from equation (1).
The terms with "x" will cancel each other, since they have equal coefficients.
You will get

         5y - 2y = 54 - 36
            
            3y   =    18

             y   =    18/3 = 6.


To find x, substitute y= 6 into equation (1). You will get  

    3x + 4*6 = 54  --->  3x = 54 - 30 = 24  --->  x = 24/3 = 8.


<U>ANSWER</U>.  x= 8,  y= 6.


<U>CHECK</U>.  To check, substitute the found values into given equations; 
        calculate left sides and compare with right sides.
</pre>

Solved.


---------------------


It looks like you need to learn &nbsp;(to get familiar with) &nbsp;the general theory/technique  on solving systems of two equations in two unknown.


In this site I developed such lessons for beginner students. &nbsp;These lessons are

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


Consider these lessons as your textbook, &nbsp;your handbook, &nbsp;your guide and your &nbsp;(free of charge) &nbsp;home teacher.


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.