Question

Given that y is a solution to the simultaneous equations:
4x2 + y2 + 10y = 47
2x - y = 5
what is the value of y when x > 0? ​

Answer 1

$\displaystyle \left \{ {{4x^2+y^2+10y=47} \atop {2x-y=5}} \right.~~~\Rightarrow~~~\left \{ {{4x^2-4xy+y^2+10y+4xy=47} \atop {2x-y=5}} \right.\\ \\ \\ \left \{ {{(2x-y)^2+10y+4xy=47} \atop {2x-y=5}} \right.~~~\Rightarrow~~~\left \{ {{5^2+10y+4xy=47} \atop {y=2x-5}} \right.\\ \\ 25+10\cdot(2x-5)+4x\cdot (2x-5)=47\\ \\ 25+20x-50+8x^2-20x=47\\ \\ 8x^2=72\\ \\ x^2=9\\ \\ x=\pm3$

$if~~x=-3~~~ than~~~y=2\cdot (-3)-5=-11\\ \\ if ~~ x=3~~~ than~~~ y=2\cdot 3-5=1$

$y=1,~~~ when~~~ x0$