If we let x equal one of the numbers, and we let y equal the other number, we can define the equation as [tex]x+y=-134[/tex]. Since we know, though, that the numbers are even and consecutive integers, we can say that [tex]y=x+2[/tex]. We can then substitute our new value of y into the first equation which becomes [tex]x+x+2=-134[/tex]. It can then be simplified as follows:
[tex]x+x+2=-134 \\ 2x+2=-134 \\ 2x=-136 \\ x=-68[/tex].
We have now solved for x, but we still need to know what y is, so we need the equation [tex]y=x+2[/tex] which we can evaluate and solve for y.
[tex]y=x+2 \\ y=-68+2 \\ y=-66[/tex]
Now we have the two consecutive even integers whose sum is -134. They are -68 and -66.
