Answer:
The system of equations has no solution.
NO SOLUTION!
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}y=-\frac{1}{2}x+4\\ x+2y=-8\end{bmatrix}[/tex]
Arrange equation variables for elimination
[tex]\begin{bmatrix}y+\frac{1}{2}x=4\\ 2y+x=-8\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}y+\frac{1}{2}x=4\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:2y+x=8[/tex]
[tex]\begin{bmatrix}2y+x=8\\ 2y+x=-8\end{bmatrix}[/tex]
subtracting equation 2y+x=8 from 2y+x = -8
[tex]2y+x=-8[/tex]
[tex]-[/tex]
[tex]\underline{2y+x=8}[/tex]
[tex]0=-16[/tex]
so the equations become
[tex]\begin{bmatrix}2y+x=8\\ 0=-16\end{bmatrix}[/tex]
0 = -16 is false, therefore the system of equations has no solution.
NO SOLUTION!
The diagram is also attached below.
