Given the ordered pair [tex]\((-4, 0)\)[/tex] and the system of equations:
[tex]\[
\left\{\begin{array}{l}
2x + y = -8 \\
x - y = -4
\end{array}\right.
\][/tex]
Let's evaluate each equation:
### First Equation: [tex]\(2x + y = -8\)[/tex]
Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 0\)[/tex] into the first equation:
[tex]\[
2(-4) + 0 = -8
\][/tex]
[tex]\[
-8 = -8
\][/tex]
The ordered pair [tex]\((-4, 0)\)[/tex] satisfies the first equation because the left-hand side equals the right-hand side. So, the statement "The ordered pair [tex]\((-4,0)\)[/tex] is a solution to the first equation because it makes the first equation true." is true.
### Second Equation: [tex]\(x - y = -4\)[/tex]
Substitute [tex]\(x = -4\)[/tex] and [tex]\(y = 0\)[/tex] into the second equation:
[tex]\[
-4 - 0 = -4
\][/tex]
[tex]\[
-4 = -4
\][/tex]
The ordered pair [tex]\((-4, 0)\)[/tex] satisfies the second equation because the left-hand side equals the right-hand side. So, the statement "The ordered pair [tex]\((-4,0)\)[/tex] is a solution to the second equation because it makes the second equation true." is true.
### Solution to the System
Since [tex]\((-4, 0)\)[/tex] satisfies both equations, it is a solution to the system. Therefore, the statement "The ordered pair [tex]\((-4,0)\)[/tex] is not a solution to the system because it makes at least one of the equations false." is false.
Conversely, the statement "The ordered pair [tex]\((-4,0)\)[/tex] is a solution to the system because it makes both equations true." is true.
### Conclusion
The correct statements about the ordered pair [tex]\((-4,0)\)[/tex] and the system of equations are:
1. The ordered pair [tex]\((-4,0)\)[/tex] is a solution to the first equation because it makes the first equation true.
2. The ordered pair [tex]\((-4,0)\)[/tex] is a solution to the second equation because it makes the second equation true.
3. The ordered pair [tex]\((-4,0)\)[/tex] is a solution to the system because it makes both equations true.
