Question 967533

You need to solve the system of two linear equations in 2 unknowns


{{{system(8x + 7y = -11,
4x - 3y = 14)}}}


Multiply the second equation by  2  and then distract from the first equation.  You will get 


  8x + 7y = -11,
-
  8x - 6y =  28
  -------------
      13y =  28 + 11 = 39.


Hence,  y = {{{39/13}}} = 3.


Now, substitute the found value of  y = 3  into the either equation of your original system,  for example,  into the first equation.  You will get 


8x +7*3 = -11,   or


8x + 21 = -11,   or


8x = -11 - 21 = -32.


Hence,  x = {{{(-32)/8}}} = -4.


<B>Answer</B>. &nbsp;The solution of the system is x = -4, y = 3.


We applied here the &nbsp;<B>Elimination method</B>. 


For solving systems of two linear equations in three unknowns see the lessons 

&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/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>Geometry interpretation of the linear system of two equations in two unknowns</A> &nbsp;and

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF =http://www.algebra.com/algebra/homework/coordinate/lessons/Solving-word-probs-using-linear-systems-of-two-eqns-with-two-unknowns.lesson>Solving word problems using linear systems of two equations in two unknowns</A>.