Answer
no solution
Work Step by Step
Using the properties of equality, the first equation, $
x-4y=4
,$ is equivalent to
\begin{array}{l}\require{cancel}
x=4y+4
.\end{array}
Substituting $x=4y+4$ into the second equation results to
\begin{array}{l}\require{cancel}
\dfrac{1}{8}x-\dfrac{1}{2}y=3
\\\\
\dfrac{1}{8}\left( 4y+4 \right)-\dfrac{1}{2}y=3
\\\\
8\left[ \dfrac{1}{8}\left( 4y+4 \right)-\dfrac{1}{2}y \right]=3(8)
\\\\
1(4y+4)-4(y)=3(8)
\\\\
4y+4-4y=24
\\\\
4y-4y=24-4
\\\\
0=20
\text{ (FALSE)}
.\end{array}
Since the solution above ended with a FALSE statement, then there is $\text{
no solution
}$ to the given system of equations.
