Do i have to add an auxiliary variable when adding a new equality constraint at a LP?

Question

For example I have the following problem: \begin{align} &\textrm{min z} = -2x_1 -x_2 +x_3 \\ &\textrm{s.t.} \\ & \qquad x_1 +2x_2 +x_3 \leq 8 \\ & \\ &\quad -x_1 +x_2 -2x_3 \leq 4 \\ & \\ &x_i \geq 0, i = 1,…,3 \end{align}

with the following optimal tableau:

-z  x1  x2  x3  s1  s2   RHS

-1  0   3   3   2   0    -16

 0  1   2   1   1   0      8

 0  0   3  -1   1   1     12

Let's say I want to add the following new constraint: $x_1 +x_2 = 3$.

Do I have to introduce an 'a' variable at my new tableau before I start doing E.R.O, to reoptimise the tableau?