To determine for which system of equations [tex]\((-2, 2)\)[/tex] is a solution, we need to substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 2\)[/tex] into each system and check if both equations in the system are satisfied.
### System A:
[tex]\[
\begin{cases}
3x - 5y = -16 \\
-2x + 3y = 10
\end{cases}
\][/tex]
Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 2\)[/tex]:
1. [tex]\(3(-2) - 5(2) = -6 - 10 = -16\)[/tex], which is true.
2. [tex]\(-2(-2) + 3(2) = 4 + 6 = 10\)[/tex], which is true.
Both equations are satisfied.
### System B:
[tex]\[
\begin{cases}
-4x + 2y = 6 \\
2x - 3y = 10
\end{cases}
\][/tex]
Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 2\)[/tex]:
1. [tex]\(-4(-2) + 2(2) = 8 + 4 = 12\)[/tex], which is not equal to 6.
2. [tex]\(2(-2) - 3(2) = -4 - 6 = -10\)[/tex], which is not equal to 10.
The first equation is not satisfied.
### System C:
[tex]\[
\begin{cases}
4x + 3y = 2 \\
5x + 4y = -2
\end{cases}
\][/tex]
Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 2\)[/tex]:
1. [tex]\(4(-2) + 3(2) = -8 + 6 = -2\)[/tex], which is not equal to 2.
2. [tex]\(5(-2) + 4(2) = -10 + 8 = -2\)[/tex], which is true.
The first equation is not satisfied.
### System D:
[tex]\[
\begin{cases}
6x + 5y = -2 \\
-8x + 5y = -6
\end{cases}
\][/tex]
Substitute [tex]\(x = -2\)[/tex] and [tex]\(y = 2\)[/tex]:
1. [tex]\(6(-2) + 5(2) = -12 + 10 = -2\)[/tex], which is true.
2. [tex]\(-8(-2) + 5(2) = 16 + 10 = 26\)[/tex], which is not equal to -6.
The second equation is not satisfied.
### Conclusion:
The point [tex]\((-2, 2)\)[/tex] satisfies both equations in system A:
[tex]\[
\begin{cases}
3x - 5y = -16 \\
-2x + 3y = 10
\end{cases}
\][/tex]
Thus, the correct system of equations is System A.
