# Help with solving system of inequalities?

8x+4y ≥ 10
3x-6y > 12

+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)

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

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.