Question 984964


It is good that you placed only  5  problems in one request and not the entire textbook :)

In any case,  I will solve here for you only one problem,  namely,  the first one.


1.  Solve the system of equations by elimination


{{{system(2x^2 + 6y^2 = 168,
2x^2 + y^2 = 43)}}}.


Distract the second equation from the first one  (this is the elimination step).  You will have


{{{5y^2}}} = {{{168-43}}} = {{{125}}}.


Hence,  {{{y^2}}} = {{{125/5}}} = {{{25}}}.

Therefore,  {{{y}}} = +/-5.


Now substitute the found value of &nbsp;<B>y</B>&nbsp; into the first system's equation. &nbsp;You will get 


{{{2x^2}}} + {{{6*25}}} = {{{168}}},


{{{2x^2}}} + {{{150}}} = {{{168}}},


{{{2x^2}}} = {{{168}}} - {{{150}}} = {{{18}}}.


{{{x^2}}} = {{{18/2}}} = {{{9}}}.


x = +/-3.


<B>Answer</B>. &nbsp;&nbsp;x = +/-3, y = +/-5.