Answer
$x=10^4, y=5$
Work Step by Step
We are given the system:
$\begin{cases}
\log x^2=y+3\\
\log x=y-1
\end{cases}$
We use the addition method. Multiply Equation 2 by -1 and add it to Equation 1.
$\log x^2 - \log x=4$
Using the Quotient rule of logarithmic property, $\log b -\log c = \log \frac{b}{c}$, we can simplify the equation as follows.
$\log \frac{x^2}{x}=4,\\
\log x =4$
Using the Inverse of exponent rule of logarithmic property,$b^{\log_{b}a}=a$. by raising both sides of the equation to the power of $10$, we can get an answer for $x$.
$10^{\log x}=10^4,\\
x=10^4$.
back substituting $x$ into the original Equation we can get answer for $y$.
$\log 10^4=y-1,\\
4 \log 10=y-1,\\
y=5$.
Therefore, the answer is:
$x=10^4, y=5$
