Question

Solve the following systems of equations.
${\log }_{4}x-{\log }_{2}y=0,x^2-5y^2+4=0$

Answer 1

${\log }_{4}x-{\log }_{2}y=0x^2-5y^2+4=0$

$\frac{1}{2}{\log }_{2}x-{\log }_{2}y=0$

${\log }_{2}x-{\log }_2{y}^2=0$

$\left(\frac{x}{y^2}\right)=1$

$x=y^2\to 1$

$x^2-5y^2+4=0\to 2$

Solving $1$ and $2$

$x^2-5x+4=0$

$(x-4)(x-1)=0$

$x=4,1$

$y^2=4,1$

$y=\pm 2,\pm 1$

$(x,4):(1,1),(1,-1),(4,+2),(4,-2)$