Let's analyze the given problem.
We are given a system of simultaneous linear equations and need to determine which specific system of equations the ordered pair [tex]\((-2, -4)\)[/tex] satisfies.
To begin, the system of equations can be represented as follows:
1. [tex]\(a_1 \cdot x + b_1 \cdot y = c_1\)[/tex]
2. [tex]\(a_2 \cdot x + b_2 \cdot y = c_2\)[/tex]
We need to find the coefficients [tex]\(a_1, b_1, c_1, a_2, b_2, \text{and } c_2\)[/tex] for which the pair [tex]\((x, y) = (-2, -4))\)[/tex] satisfies both equations of the system.
Let's evaluate each system of equations one by one:
### System 1
1. [tex]\(x + 2y = -6\)[/tex]
2. [tex]\(3x + 4y = -14\)[/tex]
Substituting [tex]\(x = -2\)[/tex] and [tex]\(y = -4\)[/tex]:
For the first equation:
[tex]\[
-2 + 2(-4) = -2 - 8 = -10 \neq -6
\][/tex]
Thus, the pair [tex]\((-2, -4)\)[/tex] does not satisfy System 1.
### System 2
1. [tex]\(2x + 3y = -12\)[/tex]
2. [tex]\(5x + 6y = -24\)[/tex]
Substituting [tex]\(x = -2\)[/tex] and [tex]\(y = -4\)[/tex]:
For the first equation:
[tex]\[
2(-2) + 3(-4) = -4 - 12 = -16 \neq -12
\][/tex]
Therefore, the pair [tex]\((-2, -4)\)[/tex] does not satisfy System 2.
### System 3
1. [tex]\(-2x - y = 6\)[/tex]
2. [tex]\(-4x - 3y = 14\)[/tex]
Substituting [tex]\(x = -2\)[/tex] and [tex]\(y = -4\)[/tex]:
For the first equation:
[tex]\[
-2(-2) - (-4) = 4 + 4 = 8 \neq 6
\][/tex]
Hence, the pair [tex]\((-2, -4)\)[/tex] does not satisfy System 3.
### System 4
1. [tex]\(x - y = -2\)[/tex]
2. [tex]\(2x - 4y = -4\)[/tex]
Substituting [tex]\(x = -2\)[/tex] and [tex]\(y = -4\)[/tex]:
For the first equation:
[tex]\[
-2 - (-4) = -2 + 4 = 2 \neq -2
\][/tex]
So, the pair [tex]\((-2, -4)\)[/tex] does not satisfy System 4.
Reviewing all the systems of equations reveals that none of them satisfy the pair [tex]\((-2, -4)\)[/tex].
Therefore, the ordered pair [tex]\((-2, -4)\)[/tex] is not a solution to any of the given systems of equations.
