Solve the following system of linear equations by graphing: \[ \begin{array}{r}-6 x+6 y=12 \\ 2 x+2 y=-24\end{array} \] Answer

To solve the system of equations by graphing, let's first rewrite both equations in slope-intercept form (y = mx + b). 1. For the first equation: \[-6x + 6y = 12\] Rearranging gives: \[6y = 6x + 12\] \[y = x + 2\] 2. For the second equation: \[2x + 2y = -24\] Rearranging gives: \[2y = -2x - 24\] \[y = -x - 12\] Now you'll want to graph both equations. - The first equation \(y = x + 2\) has a slope of 1 and a y-intercept of 2. Plot the point (0, 2) and another point by choosing x = 2, resulting in (2, 4). - The second equation \(y = -x - 12\) has a slope of -1 and a y-intercept of -12. Plot the point (0, -12) and another point by choosing x = -2, resulting in (-2, -10). When you draw the lines based on these points, you'll notice they intersect at the point (-10, -8). Thus, the solution to the system of equations is the point \((-10, -8)\).