Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,891 users

Help with solving system of inequalities?

0 votes
8x+4y ≥ 10
3x-6y > 12
Please explain too?:)
asked Mar 6, 2013 in ALGEBRA 2 by dkinz Apprentice

2 Answers

+1 vote

8x + 4y ≥ 10 - (1)

3x - 2y > 12 - (2)

Multiply each side by 3 in the inequality -(1)

3(8x + 4y) ≥ 3(10)

24x + 12y ≥ 30 -(3)

Multiply each side by 8 in the  inequality -(2)

8(3x - 6y) > 8(12)

24x - 48y > 96

Multyply each side by negitive one (4)

-24x + 48y < -96 -(4)

add (3) and (4)

Therefore 0x + 60y  = -66

Divide each side by 60

Therefore y = -66/60

simplify y = -11/10

Substitute y = -11/10  from  inequation (1)

8x + 4(-11/10) =10

8x = 10 + 44/10

8x = 144/10

Divide each side by 8

Therefore x = 18/10

Substitute x = 18/10 and y =-11/10 inequality -(1)

8(18/10) + 4(-11/10) ≥ 10

144/10 + (-44/10) ≥ 10

Multiply each side by 10

144 + (-44) ≥ 10(10)

144 - 100  ≥ 100

100 ≥ 100

100 = 100

(1) inequality is right choice

3x -6y >12

Substitute x = 18/10 and y =-11/10 inequality -(2)

3(18/10) - 6(-11/10) > 12

simplify

54/10 + 66/10 > 12

Multiply each side by 10

54 + 66 >12(10)

120 > 120

(2) inequality is a wrong choice

 

answered Mar 9, 2013 by diane 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 May 31, 2014 by david Expert

Related questions

asked Sep 11, 2014 in ALGEBRA 2 by anonymous
...