To determine which of the given systems of equations has the solution [tex]\((-1, 5)\)[/tex], we need to substitute [tex]\(x = -1\)[/tex] and [tex]\(y = 5\)[/tex] into each system and see which one satisfies all equations in that system.
### System 1:
[tex]\[
\begin{array}{l}
y = 3x + 8 \\
y = -x + 4
\end{array}
\][/tex]
Substitute [tex]\(x = -1\)[/tex] and [tex]\(y = 5\)[/tex] into both equations:
1. [tex]\(5 = 3(-1) + 8 \)[/tex]
[tex]\[
5 = -3 + 8 = 5 \quad \text{True}
\][/tex]
2. [tex]\(5 = -(-1) + 4 \)[/tex]
[tex]\[
5 = 1 + 4 = 5 \quad \text{True}
\][/tex]
Both equations are satisfied. So, System 1 has the solution [tex]\((-1, 5)\)[/tex].
### System 2:
[tex]\[
y = -x - 4
\][/tex]
Substitute [tex]\(x = -1\)[/tex] and [tex]\(y = 5\)[/tex] into the equation:
[tex]\[
5 = -(-1) - 4 \][/tex]
[tex]\[
5 = 1 - 4 = -3 \quad \text{False}
\][/tex]
The equation is not satisfied, so System 2 does not have the solution [tex]\((-1, 5)\)[/tex].
### System 3:
[tex]\[
\begin{array}{l}
y = 3x - 8 \\
y = -x + 4
\end{array}
\][/tex]
Substitute [tex]\(x = -1\)[/tex] and [tex]\(y = 5\)[/tex] into both equations:
1. [tex]\(5 = 3(-1) - 8 \)[/tex]
[tex]\[
5 = -3 - 8 = -11 \quad \text{False}
\][/tex]
2. [tex]\(5 = -(-1) + 4 \)[/tex]
[tex]\[
5 = 1 + 4 = 5 \quad \text{True}
\][/tex]
The first equation is not satisfied. So, System 3 does not have the solution [tex]\((-1, 5)\)[/tex].
### System 4:
[tex]\[
\begin{array}{l}
y = 3x - 8 \\
y = -x - 4
\end{array}
\][/tex]
Substitute [tex]\(x = -1\)[/tex] and [tex]\(y = 5\)[/tex] into both equations:
1. [tex]\(5 = 3(-1) - 8 \)[/tex]
[tex]\[
5 = -3 - 8 = -11 \quad \text{False}
\][/tex]
2. [tex]\(5 = -(-1) - 4 \)[/tex]
[tex]\[
5 = 1 - 4 = -3 \quad \text{False}
\][/tex]
Both equations are not satisfied. So, System 4 does not have the solution [tex]\((-1, 5)\)[/tex].
Thus, the correct system of equations that has the solution [tex]\((-1, 5)\)[/tex] is:
[tex]\[
\begin{array}{l}
y = 3x + 8 \\
y = -x + 4
\end{array}
\][/tex]
