let 'x' and 'y' be two numbers that have a sum of -10 and a difference of -2, then, we have the following system of equations:
[tex]\begin{gathered} x+y=-10 \\ x-y=-2 \end{gathered}[/tex]notice that if we add both equations at the same time, we get:
[tex]\begin{gathered} x+y=-10 \\ x-y=-2 \\ --------- \\ 2x=-12 \\ \Rightarrow x=\frac{-12}{2}=-6 \\ x=-6 \end{gathered}[/tex]now that we have that x = -6, we can find the value of y substituting x = -6 on any equation:
[tex]\begin{gathered} -6+y=-10 \\ \Rightarrow y=-10+6=-4 \\ y=-4 \end{gathered}[/tex]therefore, x = -6 and y = -4. Next, we have that the product is (-6)(-4) = 24
