Help with solving system of inequalities?

Question

8x+4y ≥ 10
3x-6y > 12

Answer 1

8x+4y ≥ 10
y ≥ -2x + 5/2
first graph the line y = -2x + 5/2 and the line is solid and shade the region above the line
3x-6y > 12
y < 1/2x -2
graph the line y = 1/2x -2 and the line is dotted and shade the region below the line.
The ordered pairs in the common area are the solutions of the inequality.
 

Answer 2

The inequalities are 8x + 4y  ≥ 10  and 3x  - 6y  > 12.

1) Draw the coordinate plane.

Now first inequality 8x  + 4y  ≥ 10 .

2) Graph the line y = -2x + 5/2

3) Since the inequality symbol is  ≥  the boundary is  included the solution set.

Graph the boundary of the inequality 8x  + 4y  ≥ 10  with dashed 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.

8(0) + 4(0) ≥ 10

0 ≥ 10

The statement is false.

5) Since the statement is false , shade the region except contain point (0,0),Shaded in aqua colour.

Now second inequality 3x  - 6y  > 12.

6) Graph the line y  = x/2  - 2

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

Graph the boundary of the inequality 3x  - 6y  > 12 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.

3(0) - 6(0) > 12

0 > 12

The statement is false.

9) Since the statement is false, shade the region contain point (0,0), shaded in pink colour.

Graph :

The solution of the system is the set of ordered pairs in the intersection of the graph of 3x  - 6y  > 12  and 8x  + 4y  ≥ 10. This region is shaded in light blue color.

The region where the shadings overlap is the solution to the system of inequalities.