You can translate the two statements from English to math:
stackrel(x+y) overbrace"The sum of two numbers"" " stackrel(=) overbrace"is"" " stackrel(-28) overbrace"-28."
stackrel(x*y) overbrace"The product of the same two numbers"" " stackrel(=) overbrace"is"" " stackrel(96) overbrace"96."
Now we can create a system of equations:
{(x+y=-28, qquad(1)), (x*y=96, qquad(2)):}
Now, solve for x in equation (1):
color(white)(=>)x+y=-28
=>x=-28-y
Plug this new x value into equation (2):
color(white)(=>)x*y=96
=>(-28-y)*y=96
color(white)(=>)-28y-y^2=96
color(white)(=>)-y^2-28y-96=0
color(white)(=>)y^2+28y+96=0
color(white)(=>)(y+24)(y+4)=0
color(white)(=>)y=-4,-24
Lastly, plug both of these y values back into equation (1):
For y=-4:
color(white)(=>)x+y=-28
=>x-4=-28
color(white)(=>)x=-24
And for y=-24:
=>x-24=-28
color(white)(=>)x=-4
Finally, we see that there are two solutions which are the same: (-4,-24) and (-24,-4).
This means that the two numbers are -4 and -24.
