Respuesta :
Answer
System of equation = m + n = -15, m - n = 7
The two numbers = -4, -11
Explanation
Let variables m and n represent the two numbers.
The sum of variables m and n is negative fifteen, This implies;
[tex]m+n=-15----i[/tex]One number is seven less than the other implies;
[tex]\begin{gathered} m-n=7----ii \\ \text{Where;} \\ m\text{ is the greater number and} \\ n\text{ is the lesser number} \end{gathered}[/tex]Hence, the system of equations that describe the situation is
[tex]\begin{gathered} m+n=-15----i \\ m-n=7-----ii \end{gathered}[/tex]To find the two numbers, use the elimination method.
[tex]\begin{gathered} (i)+(ii) \\ \Rightarrow m+m+n+(-n)=-15+7 \\ 2m=-8 \\ \text{Divide both sides by 2} \\ \frac{2m}{2}=-\frac{8}{2} \\ m=-4 \end{gathered}[/tex]To get n, substitute m = -4 into (i)
[tex]\begin{gathered} \text{Recall (i)} \\ m+n=-15---i \\ \Rightarrow-4+n=-15 \\ \text{Collect the like terms} \\ n=-15+4 \\ n=-11 \end{gathered}[/tex]Therefore, the two numbers = -4, -11
