Question 1097061
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The coefficients of the first equation are PROPORTIONAL to the coefficients of the second equation with the proportionality coefficient of {{{1/12}}}.


Then the necessary and sufficient condition for the system to have a solution is that the right side terms are proportional with the same coefficient.


It gives an equation for the term "a":  {{{a*(1/12)}}} = 2, which gives a = 24.


At the same time, this condition is a necessary and sufficient for the system to have INFINITE number of solutions.
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See the lesson

&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> 

in this site.


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 lesson is 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.