Let's analyze the given system of equations step-by-step. We are given four different equations:
1. [tex]\( y = -1 \)[/tex]
2. [tex]\( y = -3 \)[/tex]
3. [tex]\( y = 1 \)[/tex]
4. [tex]\( y = 3 \)[/tex]
To determine a value for [tex]\(y\)[/tex] that satisfies all four equations simultaneously, let's examine each equation.
1. Considering [tex]\(y = -1\)[/tex]:
- Here, [tex]\( y \)[/tex] must equal [tex]\(-1\)[/tex].
2. Considering [tex]\(y = -3\)[/tex]:
- In this case, we need [tex]\( y \)[/tex] to be [tex]\(-3\)[/tex].
3. Considering [tex]\(y = 1\)[/tex]:
- Now, [tex]\( y \)[/tex] should be [tex]\(1\)[/tex].
4. Considering [tex]\(y = 3\)[/tex]:
- Finally, [tex]\( y \)[/tex] should be [tex]\(3\)[/tex].
To satisfy all these given equations simultaneously, we would need a single value of [tex]\( y \)[/tex] that satisfies:
[tex]\[
y = -1 \quad \text{and} \quad y = -3 \quad \text{and} \quad y = 1 \quad \text{and} \quad y = 3
\][/tex]
However, each of these equations represent different values for [tex]\( y \)[/tex]:
- [tex]\( y \)[/tex] must be [tex]\(-1\)[/tex] according to the first equation.
- [tex]\( y \)[/tex] must be [tex]\(-3\)[/tex] according to the second equation.
- [tex]\( y \)[/tex] must be [tex]\(1\)[/tex] according to the third equation.
- [tex]\( y \)[/tex] must be [tex]\(3\)[/tex] according to the fourth equation.
Clearly, these prescribed values of [tex]\( y \)[/tex] are contradictory because one value of [tex]\( y \)[/tex] cannot simultaneously equal [tex]\(-1\)[/tex], [tex]\(-3\)[/tex], [tex]\(1\)[/tex], and [tex]\(3\)[/tex]. These values are distinct and, hence, cannot be equal to each other.
Therefore, after analyzing the equations, we conclude that:
No single value of [tex]\( y \)[/tex] can satisfy all four given equations simultaneously.
