Iam not understanding any of this math stuff. how would you solve and graph systems of inequalities? for example, x+y< _-1 x+y> _3

x + y ≥ 3

Step-by-step explanation:

(1)  x + y ≥ -1

(2) x + y ≥  3

Step 1. Graph the equalities

(3) x + y = -1

(4) x + y =  3

For Equation (3)

x   -5   0    5

y    4  -1    -6

For Equation (4)

x  -5   0   5

y   8   3  -2

We get the graphs in Fig.1.

Step 2. Check one or two points to find those in the solution set.

Check the point (10,0).

For Equation (1),  

10 + 0 ≥ -1. TRUE. (10,0) is in the solution set.

Shade the region to the right of the red solid line and including the line, red (Fig. 2).

For Equation (2),

10 + 0 ≥ 3. TRUE. (10,0) is in the solution set.

Shade the region to the right of the blue solid line and including the line, blue (Fig. 3).

Step 3. Identify the solution set for the system of inequalities.

Fig. 4 shows that the solution set is the purple region of the plane in which the two sets overlap.

Every point that satisfies Inequality (2) also satisfies Inequality (1).

The solution set is x + y ≥ 3.