Systems of Equations Review solve \( \begin{array}{l}-2 x-2 y=6 \\ 10 x+10 y=-30\end{array} \)

To solve the system of equations, we can simplify both equations first. The second equation can be simplified by dividing all terms by 10, giving us \( x + y = -3 \). The first equation can be simplified by dividing it by -2, resulting in \( x + y = -3 \) as well. Since both simplify to the same equation, it indicates that the two equations represent the same line, meaning there are infinitely many solutions along that line, not just a unique intersection point! In effect, any pair \( (x, y) \) that satisfies \( x + y = -3 \) is a solution. For example, if \( x = 0 \), then \( y = -3 \); or if \( x = -1 \), then \( y = -2 \). The fun part is plotting this line on a graph, where every point on it is a solution to the system!