stem of linear equations shown below have a solution? Explain- \[ \left\{\begin{array}{l}x+7 y=8 \\ 7 x-y=-2\end{array}\right. \]

To determine if the system of linear equations has a solution, we can analyze the equations. The first equation, \(x + 7y = 8\), can be rearranged to express \(x\) in terms of \(y\) as \(x = 8 - 7y\). The second equation, \(7x - y = -2\), can be rearranged to express \(y\) in terms of \(x\) as \(y = 7x + 2\). By substituting the expression for \(x\) into the second equation, we can find a specific point \((x, y)\) that satisfies both, indicating that the system has a solution. Let's actually solve it step-by-step. Substituting \(x = 8 - 7y\) into \(y = 7x + 2\) gives: \[y = 7(8 - 7y) + 2\] \[y = 56 - 49y + 2\] \[y + 49y = 58\] \[50y = 58\] Thus, \(y = \frac{58}{50} = \frac{29}{25}\). Now substitute \(y\) back into the first equation to find \(x\): \[x + 7\left(\frac{29}{25}\right) = 8\] \[x + \frac{203}{25} = 8\] \[x = 8 - \frac{203}{25} = \frac{200}{25} - \frac{203}{25} = -\frac{3}{25}\]. So, this system does indeed have a solution \(\left(-\frac{3}{25}, \frac{29}{25}\right)\).