Answer
Infinitely many solutions
Solution set $(2+4y,y)$, where $y$ arbitrary
Work Step by Step
Let's note the equations:
$$2x-8y =4 ~~~(1) \\ x-4y=2~~~(2)$$
We will apply the Elimination Method.
We need to multiply the second equation by $-2$ and by doing so the second equation becomes: $$-2x+8y =-4 ~~~~(3)$$
Next we add equations $(1)$ and $(3)$ in order to eliminate $x$ as follows:
$2x-8y-2x+8y=4-4 \\ 0=0 $
As we can notice that both variables are eliminated which implies that the system of equations has infinitely many solutions and we can say that the equations refer to the same line.
In order to Isolate $x$ from equation $(2)$, we will solve for $x$ as follows:
(Adding $4y$ to both sides of the equation)
$$x-4y=2 \implies x-4y+4y=2+4y$$
or, $$x=2+4y$$
Hence, the required solution set with $y$ arbitrary is equivalent to: $$(2+4y,y)$$.
