Answer
Inconsistent
Work Step by Step
We are given the system of equations:
$\begin{cases}
x-3y+4=0\\
\dfrac{1}{2}x-\dfrac{3}{2}y+\dfrac{4}{3}=0
\end{cases}$
Multiply the second equation by 6 to clear denominators and bring the system to the standard form:
$\begin{cases}
x-3y+4=0\\
6\left(\dfrac{1}{2}x-\dfrac{3}{2}y+\dfrac{4}{3}\right)=6(0)
\end{cases}$
$\begin{cases}
x-3y+4=0\\
3x-9y+8=0
\end{cases}$
$\begin{cases}
x-3y=-4\\
3x-9y=-8
\end{cases}$
Use the elimination method. Multiply the first equation by -3 and add it to the second to eliminate $x$ and find $y$:
$-3(x-3y)+3x-9y=-3(-4)-8$
$-3x+9y+3x-9y=4$
$0=4$
We got a false statement; therefore the system is inconsistent.
