what is -x+3y>-3 and y<2x-8

Question

-x+3y>-3 and y<2x-8.

Answer 1

The system of inequalities are - x + 3y > - 3 and y < 2x - 8.

First inequality is - x + 3y > - 3.

The graph of the inequality - x + 3y > - 3 is the shaded region and boundary of the inequality is - x + 3y = - 3.

y > (1/3)x - 1

1. Draw the coordianate plane.

2.  Since inequality - x + 3y > - 3 symbol is >, the boundary is not included in the solution set. Graph the boundary of the inequality - x + 3y = - 3 with dotted line.

3.  To determine which half-plane to be shaded use a test point in either half-plane. A simple choice is (0, 0).

Substitute and x = 0 and y = 0 in original inequality - x + 3y > - 3.

0 + 3(0) > - 3

0 > - 3

The statement is true.

4. Since the statement is true, shade the region contains point (0, 0).

Second inequality is y < 2x - 8.

5.The graph of the inequality y < 2x - 8 is the shaded region and boundary of the inequality is y = 2x - 8.

y < 2x - 8

6.  Since inequality y < 2x - 8 symbol is <, the boundary is not included in the solution set. Graph the boundary of the inequality y = 2x - 8 with dotted line.

7.  To determine which half-plane to be shaded use a test point in either half-plane. A simple choice is (0, 0).

Substitute and x = 0 and y = 0 in original inequality y < 2x - 8.

0 < 2(0) - 8

0 < 0 - 8

0 < - 8

The statement is false.

8. Since the statement is false, shade the region does not contains point (0, 0).

Graph :

The solution of the system is the set of ordered pairs in the intersection of the graph of -x + 3y > - 3 and y <2x - 8. This region is shaded in light purple color.

Observe the graph, the intersection point is (4 . 2, 0 . 4).so,this is the solution of the system of inequalities.