Question 1199807
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<pre>

The starting system of equations is

    6x - 5y = -30     (1)
    2x + 2y =  12     (2)


Multiply equation (2) by 3 (both sides). Keep equation (1) as is.  You get

    6x - 5y = -30     (3)
    6x + 6y =  36     (4)


Now equations (3) and (4) have the same coefficient at x.
Therefore, you subtract equation (3) from equation (4), and you annihilate the terms "6x" this way.
You get then

         6y - (-5y) = 36 - (-30)

            11y     =    66

              y     =    66/11 = 6.


Then from equation (2)

    2x = 12 - 2y = 12 - 2*6 = 0.


<U>ANSWER</U>.  x = 0, y = 6.
</pre>

Solved.


You may check it that the answer is correct 
by substituting the found values in original equations.


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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> 

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/coordinate/lessons/Useful-tricks-when-solving-systems-of-2-eqns-in-2-unknowns-by-the-Subst-method.lesson>Useful tricks when solving systems of 2 equations in 2 unknowns by the Substitution method</A> 


They give you the general theory and a lot of examples which you can consider as your TEMPLATES.


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.