Question 967531


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


{{{system(4x + 3y = -10,
9x + 2y = 6)}}}


Multiply the first equation by 2 and the second equation by  -3.   Then add the obtained equations.  You will get 


    8x  + 6y = -20,
+
 -27x - 6y = -18
  -------------
 -19x         = -20 - 18 = -38.


Hence,  x = {{{(-38)/(-19)}}} = {{{38/19}}} = 2.


Now, substitute the found value of  x = 2  into the either equation of your original system,  for example,  into the first equation.  You will get 


4*2 + 3*y = -10,   or


8 + 3*y = -10,   or


3y = -10 - 8 = -18.


Hence,  y = {{{(-18)/3}}} = -6.


<B>Answer</B>. &nbsp;The solution of the system is x = 2, y = -6.


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>.