We are given the following system of equations
[tex]\begin{gathered} -\frac{1}{2}x-4y=4 \\ 2x+16y=2 \end{gathered}[/tex]
Let us solve the above system of equations using the elimination method.
Suppose we want to cancel the x terms, then we have to multiply eq.1 by 4.
[tex]4\cdot(-\frac{1}{2}x-4y=4)\Rightarrow-2x-16y=16[/tex]
Now, add the two equations
As you can see, after adding the equations we get 0 = 18 which cannot be true.
This means that no solution exists for this system of linear equations.
