Answer
Consistent
Solution set: $\left\{\left(x,y\right)|x=4-2y,y\text{ is any real number}\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
x+2y=4\\
2x+4y=8
\end{cases}$
Write the augmented matrix:
$\begin{bmatrix}1&2&|&4\\2&4&|&8\end{bmatrix}$
Perform row operations to bring the matrix to the reduced row echelon form:
$R_1=\dfrac{1}{2}r_1$
$\begin{bmatrix}1&2&|&4\\1&2&|&4\end{bmatrix}$
$R_1=-r_1+r_2$
$\begin{bmatrix}1&2&|&4\\0&0&|&0\end{bmatrix}$
The last row only contains zeroes, so the system is consistent, having infinitely many solutions.
Write the corresponding system of equations:
$\begin{cases}
x+2y=4\\
0=0
\end{cases}$
Express $x$ in terms of $y$:
$x+2y=4\Rightarrow x=4-2y$
The solution set is:
$\left\{\left(x,y\right)|x=4-2y,y\text{ is any real number}\right\}$
