Solve the following system of linear equations by graphing: \[ \begin{array}{l}4 x+4 y=16 \\ 7 x+7 y=-21\end{array} \]

To solve the system of equations by graphing, we first rewrite each equation in slope-intercept form (y = mx + b). Starting with the first equation: \[ 4x + 4y = 16 \] Divide every term by 4: \[ x + y = 4 \] Now isolate y: \[ y = -x + 4 \] Next, for the second equation: \[ 7x + 7y = -21 \] Divide every term by 7: \[ x + y = -3 \] Now isolate y: \[ y = -x - 3 \] Now that we have the equations in slope-intercept form, we can graph them: 1. The first line \( y = -x + 4 \) has a y-intercept at (0, 4) and a slope of -1. From (0, 4), you can go down 1 unit and right 1 unit to get to another point (1, 3). 2. The second line \( y = -x - 3 \) has a y-intercept at (0, -3) and a slope of -1 as well. From (0, -3), you go down 1 unit and right 1 unit to (1, -4). On graphing these two lines, you'll notice they are parallel since they both have the same slope (-1). Since parallel lines never intersect, this system of equations has no solution.