To solve the inequalities for [tex]\( y \)[/tex]:
1. Consider the first inequality:
[tex]\[
-8x + y < 1
\][/tex]
To isolate [tex]\( y \)[/tex], add [tex]\( 8x \)[/tex] to both sides:
[tex]\[
y < 8x + 1
\][/tex]
2. Next, consider the second inequality:
[tex]\[
y > -1 + 8x
\][/tex]
It simplifies as given directly, showing:
[tex]\[
y > 8x - 1
\][/tex]
Thus, the solution to the system of inequalities is:
[tex]\[
y < 8x + 1 \quad \text{and} \quad y > 8x - 1
\][/tex]
So, the solution set can be expressed as both:
[tex]\[
y < 8x + 1 \quad \text{and} \quad y > 8x - 1
\][/tex]
Therefore the inequalities simplify to:
[tex]\[
y < 8x + 1
\][/tex]
[tex]\[
y > 8x - 1
\][/tex]
which are represented in the following piece:
[tex]\[
y < 1 + 8x \quad \text{and} \quad y > -1 + 8x
\][/tex]
Thus, the correct answer choices are:
[tex]\( y < 1 + 8x \)[/tex]
and
[tex]\( y > -1 + 8x \)[/tex].
Conclusively:
[tex]\[
\boxed{y < 8x + 1 \quad \text{and} \quad y > 8x - 1}
\][/tex]
