graph the following inequalities

Question

y < x + 3
y < -2x + 4

Thank you for anyone who will kindly answer.

Answer 1

Given inequalities are y < x + 3 and y < - 2x + 4.

1) Draw the coordinate plane.

Now first inequality y < x + 3.

2) Graph the line y = x + 3

3) Since the inequality symbol is < the boundary is not included the solution set.

Graph the boundary of the inequality y < x + 3 with dotted line.

4) To determine which half plane to be shaded use a test point in either half- plane.

A simple chioce is (0,0). Substitute x  = 0 and y  = 0 in original inequality

0 < 0 + 3

0 < 3

The statement is true.

5) Since the statement is true , shade the region contain point (0,0)

Shaded in fuchsia colour.

Now second inequality y < - 2x + 4.

6) Graph the line y = - 2x + 4

7) Since the inequality symbol is < the boundary is not included the solution set.

Graph the boundary of the inequality y < - 2x + 4 with dotted line.

8) To determine which half plane to be shaded use a test point in either half- plane.

A simple chioce is (0,0). Substitute x  = 0 and y  = 0 in original inequality

0 < 0 + 4

0 < 4

The statement is true.

9) Since the statement is true , shade the region contain point (0,0)

shaded in aqua colour.

Graph :

The solution of the system is the set of ordered pairs in the intersection of the graph of y < x + 3 and y < - 2x + 4. This region is shaded in light purple color.