Question 1157052
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    11x - 5y = 10     (1)

    13x - 7y =  2     (2)


The idea of this method is to multiply each equation by some number in such a way
to make the coefficients at some variable EQUAL (or OPPOSITE).


Then by subtracting equations, we can DELETE this variable in the resulting equation.

So, we will get in this way SINGLE equation with ONLY ONE unknown, which is easy to solve.


Looking into the given equations, you see that the better and the simplest way is to multiply 
first equation by 7 and the second equation by 5.


You will get then  these two equations

    77x - 35y = 70     (3)

    65x - 35y = 10     (4)


Do you see these terms "35y" in each equations ?  They are exactly that we were going to provide (and we provided them (!) ).


Now from equation (3) subtract equation (4). The terms "-35y" will cancel each other, 
and you will get ONE SINGLE equation for the unknown x ONLY (!)

    77x - 65x = 70 - 10.


Simplify and solve it, as the equation with only one unknown x


    12x       = 60.

     x        = 60/12 = 5.


The last step is to substitute this value of x into EITHER of the two original equations.


You will get then an equation for "y" only, and you should solve it to get y.

Do it on your own.
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I completed my explanations.


Now I ask you &nbsp;&nbsp;1) &nbsp;if you do understand everything in my post,


and &nbsp;&nbsp;2) &nbsp;please inform me if you there able to complete the solution.


If you will post to me, &nbsp;PLEASE &nbsp;refer to the problem's &nbsp;ID number &nbsp;1157052;

otherwise, &nbsp;I will not know to which problem your message does relate.


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In this site, there is the lesson, explaining this technology in all details.


&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> 


It is the SECOND lesson in this short list.



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.


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It is my response to your question :   &nbsp;&nbsp;x = 5, &nbsp;y = 9.


You may check it by substituting the values into original equations.