Question

Solve the following system of equations.
$\log \sqrt{(x+y{)}^2}=1,\log y-\log |x|=\log 2$

Answer 1

$\log \sqrt{{(x+y)}^2}=1$

$\log |x+y|=1$

$(x+y)=10\to 1$

$\log y-\log \left|x\right|=\log 2$

$\log \frac{y}{\left|x\right|}=\log 2$

$y=2\left|x\right|\to 2$

$y=\{\begin{array}{c}2x;x>0\\ -2x;x<0\end{array}$

From $1$ and $2$

$|x+\left|x\right||=10$

$x>0\left|2x\right|=10x=5$

$x<0|x-x|=10$

$x=5;y=10$