Answer
$(x,4x-5)$ for any real $x$
Work Step by Step
We are given the system:
$\begin{cases}
y=4x-5\\
8x-2y=10
\end{cases}$
We will use the substitution method. Substitute the expression of $y$ from Equation 1 into Equation 2 to eliminate $y$ and determine $x$:
$\begin{cases}
y=4x-5\\
8x-2(4x-5)=10
\end{cases}$
$8x-2(4x-5)=10$
$8x-8x+10=10$
$10=10$
We got a true statement. Therefore the system's solution is:
$(x,y)$ for which $y=4x-5$
The solution can also be written:
$(x,4x-5)$ for any real $x$
