Answer:
C. 15
Step-by-step explanation:
1. First, let's solve the system of equations; [tex]-m - n = 5, m - n = -3[/tex]
Solve -m - n = 5 for m.
- [tex]-m -n = 5[/tex]
- [tex]-m-n+n=5+n[/tex]
- [tex]-m = n + 5[/tex]
- [tex]\frac{-m}{-1} = \frac{n+5}{-1}[/tex]
- [tex]m = -n - 5[/tex]
Substitute -n - 5 for m in m - n = -3.
- [tex]m - n = -3[/tex]
- [tex]-n - 5 - n = -3[/tex]
- [tex]-2n-5=-3[/tex]
- [tex]-2n-5+5=-3+5[/tex]
- [tex]-2n = 2[/tex]
- [tex]\frac{-2n}{-2} = \frac{2}{-2}[/tex]
- [tex]n = -1[/tex]
Substitute -1 for n in m = -n - 5.
- [tex]m = -n - 5[/tex]
- [tex]m = -(-1) - 5[/tex]
- [tex]m = 1 - 5[/tex]
- [tex]m = -4[/tex]
2. Okay, now that we know m = -4 and n = -1, let's solve for m^2 -n^2.
- [tex]m^2-n^2[/tex]
- [tex](-4)^2-(-1)^2[/tex]
- [tex]16 - (-1)^2[/tex]
- [tex]16 - 1[/tex]
- [tex]15[/tex]
Therefore, the answer is C. 15!
