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