Answer:
The correct option is 'No Solution'.
Step-by-step explanation:
Given the system of the equations
[tex]y=\frac{1}{2}x-1[/tex]
[tex]2x-4y=12[/tex]
solving the system of the equations
[tex]\begin{bmatrix}y=\frac{1}{2}x-1\\ 2x-4y=12\end{bmatrix}[/tex]
[tex]\mathrm{Subsititute\:}y=\frac{1}{2}x-1[/tex]
[tex]\begin{bmatrix}2x-4\left(\frac{1}{2}x-1\right)=12\end{bmatrix}[/tex]
[tex]2x-4\left(\frac{1}{2}x-1\right)=12[/tex]
[tex]2x-2x+4=12[/tex]
[tex]4=12[/tex]
as
4=12 is false, therefore the system of equations has no solution.
Therefore, the correct option is 'No Solution'.
