Answer
The system of equations is inconsistent and has no solutions.
Work Step by Step
We need to solve the given system of equations:
$x−3y+4=0~~~(1)\\ \dfrac{x}{2}-\dfrac{3y}{2}+\dfrac{4}{3}=0 ~~~(2)$
Multiply the second equation by $2$.
$x-3y+\dfrac{8}{3} =0~~~ (3)$
Re-write equation (1) as: $x=3y-4$
Substitute $x=3y-4$ into equation (3).
$(3y-4)-3y+\dfrac{8}{3} =0 \\ \dfrac{4}{3}=2$
Since $\dfrac{4}{3}$ never equals $2$, the system of equations is inconsistent and has no solutions.
