Question

Solve the following systems of equations.
$\sqrt{x^2}+y=5,y^2-x=7$

Answer 1

Given equations are,

$\sqrt{x^2}+y=5⟹x+y=5⟹x=5-y$......(i)

$y^2-x=7$.........(ii)

$⟹y^2-(5-y)=7$

$⟹y^2+y-5-7=0$

$⟹y^2+y-12=0$

$⟹(y+4)(y-3)=0$

$\therefore y=-4$ or $y=3$

$⟹x=5-(-4)=9$ or $x=5-3=2$

The required solutions are,

$(9,-4),(2,3)$