Question 950616
Make the equations exactly as described.  <s>Nothing strange here</s>.  Some lack of clarity in , "increased by four times the smaller".  That does not mean "more than" or "less than".


x and y, the numbers, {{{x<y}}}.


{{{system(y=8+4x,(y*4x)=40)}}}.
Elimination Method is not applicable here.


{{{y*x=10}}}, simplified second part.
{{{(8+4x)*x=10}}}, substituted for y from first part.
{{{(4+2x)x=5}}}
{{{2x^2+4x=5}}}
{{{2x^2+4x-5=0}}}


Factorable?
(2x____5)(x____1), no.
(2x____1)(x_____5), no.


Discriminant to prepare for general quadratic formula solution:
{{{16-4*2*(-5)}}}
{{{16+8*5}}}
{{{56}}}


{{{x=(-4+- sqrt(56))/4}}}
{{{x=(-4+- 2*sqrt(14))/4}}}
{{{x=(-2+- sqrt(14))/2}}}


Trying just the plussquare root form,
{{{y=8+4x=8+4(highlight((-2+sqrt(14))/2))}}}
{{{8+2(-2+sqrt(14))}}}
{{{8-4+2sqrt(14)}}}
{{{highlight(y=4+2*sqrt(14))}}}  for one possible combination x and y.


You can check on the other combination.