Suppose $x_i$ are binary variables, $y_j$ are arbitrary variables, $a_j$ and $b$ are constants, and I have the following linear constraints: \begin{align} x_i + \sum_j a_j y_j &\le b &&\text{for all $i$} \tag1\\ \sum_i x_i &\le 1 \tag2 \end{align} How can I replace $(1)$ with $(3)$? \begin{align} \sum_i x_i + \sum_j a_j y_j &\le b &&\text{for all $i$} \tag{3}\\ \end{align}

Suppose $x_i$ are binary variables, $y_j$ are arbitrary variables, $a_j$ and $b$ are constants, and I have the following linear constraints: \begin{align} x_i + \sum_j a_j y_j &\le b &&\text{for all $i$} \tag1\\ \sum_i x_i &\le 1 \tag2 \end{align} How can I replace $(1)$ with $(3)$? \begin{align} \sum_i x_i + \sum_j a_j y_j &\le b \tag{3}\\ \end{align}