\( \left.\begin{array}{l}\text { Solve the system of equations by graphing: } \\ \left\{\begin{array}{l}-4 x+2 y=26 \\ y\end{array}=2 x+13\right.\end{array}\right\} \) Enter your answer as a numbers. If the system is inconsistent (has no solutions), enter DNE

To solve the system of equations by graphing, we first rewrite each equation in slope-intercept form (y = mx + b). 1. The first equation: \(-4x + 2y = 26\) - Rearranging it gives: \(2y = 4x + 26\) - Dividing all terms by 2, we get: \(y = 2x + 13\) 2. The second equation is already simplified: \(y = 2x + 13\) Now we see that both equations are identical, meaning they represent the same line. Thus, there are infinitely many solutions along this line. To express this mathematically, we can choose any \(x\)-value and find the corresponding \(y\)-value. For example, if \(x = 0\), then \(y = 2(0) + 13 = 13\). Therefore, one solution is (0, 13). However, since the two equations represent the same line, we conclude that the system has infinitely many solutions. **Final answer:** Infinitely many solutions (e.g., \((0, 13)\)) or you can express it as the equation \(y = 2x + 13\).