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Help with solving system of inequalities?

0 votes

8x+4y ≥ 10
3x-6y > 12

asked Mar 2, 2013 in ALGEBRA 2 by johnkelly Apprentice

2 Answers

0 votes

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.

 

answered Mar 3, 2013 by steve Scholar
0 votes

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

1) Draw the coordinate plane.

Now first inequality 8x  + 4 ≥ 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  - 6 > 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 = 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 3 - 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.

answered Jun 2, 2014 by david Expert

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