Graph the solution set of each system of inequalities.
$2y+x\ge-5$
$y\le3+x$$x\le0$
$y\le0$

Verified step by step guidance

1. Step 1: Start by graphing the inequality 2y + x \ge -5. Rewrite it in slope-intercept form (y = mx + b) by isolating y. Subtract x from both sides to get 2y \ge -x - 5, then divide every term by 2 to get y \ge -\frac{1}{2}x - \frac{5}{2}. This represents a line with a slope of -\frac{1}{2} and a y-intercept of -\frac{5}{2}. Shade the region above this line, as the inequality is \ge.
2. Step 2: Next, graph the inequality y \le 3 + x. Again, rewrite it in slope-intercept form if necessary. This is already in the form y \le x + 3, which represents a line with a slope of 1 and a y-intercept of 3. Shade the region below this line, as the inequality is \le.
3. Step 3: Graph the inequality x \le 0. This is a vertical line at x = 0. Shade the region to the left of this line, as the inequality is \le.
4. Step 4: Graph the inequality y \le 0. This is a horizontal line at y = 0. Shade the region below this line, as the inequality is \le.
5. Step 5: The solution set of the system of inequalities is the region where all the shaded areas overlap. Identify this region on the graph, which will be bounded by the lines you have drawn and shaded according to the inequalities.