The augmented matrix that corresponds to a system of linear equations in \( x_{1} \) and \( x_{2} \) is \( \left[\begin{array}{ll|l}1 & 1 & 3 \\ 0 & 1 & 3\end{array}\right] \) \( x_{1}= \) Ex: 42 \( x_{2}= \)

To solve the system represented by the augmented matrix \( \left[\begin{array}{ll|l}1 & 1 & 3 \\ 0 & 1 & 3\end{array}\right] \), we can rewrite the equations it represents. The first row translates to the equation \( x_{1} + x_{2} = 3 \), and the second row translates to \( x_{2} = 3 \). Plugging \( x_{2} = 3 \) into the first equation gives us \( x_{1} + 3 = 3 \), leading to \( x_{1} = 0 \). In terms of real-world applications, systems of linear equations like this can represent various scenarios, such as finding the intersection point of two lines, optimizing production in business, or even determining resource allocation in a project. In this case, \( x_{1} = 0 \) and \( x_{2} = 3 \) could represent a situation where one type of resource is absent, while another is fully utilized!