y>x-5 solve each system of linear ineualities

Question

1.)  y< x

y>x-5

2.)3y-x<9

3y-x>-9

3. y<3x-2

y>-x+3

4.x-2y<5

5x+2y>3

x+y<4

Answer 1

(1) the inequalities are y  ≤ x  and y  > x  - 5.

1) Draw the coordinate plane.

Now first inequality y  ≤ x .

2) Graph the line y = x 

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

Graph the boundary of the inequality y  ≤ x  with dashed line.

4) To determine which half plane to be shaded use a test point in either half- plane.

A simple chioce is (1,-1). Substitute x  = 1 and y  = -1 in original inequality

-1 ≤ 1

The statement is true.

5) Since the statement is true , shade the region contain point (1,-1),Shaded in fuchsia colour.

Now second inequality y  > x - 5.

6) Graph the line y  = x  - 5

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

Graph the boundary of the inequality y > x - 5 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

0 > 0 - 5

0 > -5

The statement is true.

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

Graph :

The solution of the system is the set of ordered pairs in the intersection of the graph of y  ≤ x  and y  > x  - 5.. This region is shaded in light purple color.

Comments

Sorry typo mistake,

Graph the boundary of the inequality y  ≤ x  with solid line.

Answer 2

(2) The inequalities are 3y - x  ≤ 9  and 3y - x  ≥ -9

Rearrange the inequalities so that solves for y  , That's the slope intercept form and it will make the boundary line easier to graph.

1) Draw the coordinate plane.

Now first inequality 3y - x  ≤ 9 .

3y  ≤ x  +  9

y  ≤ x /3 + 3

2) Graph the line y = x/3 + 3

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

Graph the boundary of the inequality y  ≤ x / 3 + 3  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

0 ≤ 0/3 + 3

0 ≤  3

The statement is true.

5) Since the statement is true , shade the region contain point (0,0),Shaded in fuchsia colour.

Now second inequality 3y - x  ≥ -9

3y  ≥ x  - 9

y  ≥ x /3 - 3

6) Graph the line y  = x /3  - 3

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

Graph the boundary of the inequality y  ≥ x /3 - 3 with dashed 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

0 ≥ 0/3 - 3

0 ≥ -3

The statement is true.

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

Graph :

The solution of the system is the set of ordered pairs in the intersection of the graph of

3y - x  ≤ 9  and 3y - x  ≥ -9. This region is shaded in light purple color.

Answer 3

(3) The inequalities are y  < 3x - 2  and y  > - x  + 3.

1) Draw the coordinate plane.

Now first inequality y  < 3x - 2.

2) Graph the line y = 3x - 2

3) Since the inequality symbol is  <  the boundary is  not included the solution set.

Graph the boundary of the inequality y  < 3x - 2  with dotted 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

0 ≤ -2

The statement is false.

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

Now second inequality y  > - x  + 3..

6) Graph the line y  = - x  + 3

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

Graph the boundary of the inequality y  > - x + 3 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

0 > -0 + 3

0 > 3

The statement is false.

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

Graph :

The solution of the system is the set of ordered pairs in the intersection of the graph of

y  < 3x - 2  and y  > - x  + 3. This region is shaded in light purple color.

 

Answer 4

(4) The inequalities are 4x  - 2y < 5 , 5x + 2y  > 3 and x + y  < 4.

Rearrange the inequalities so that solves for y  , That's the slope intercept form and it will make the boundary line easier to graph.

1) Draw the coordinate plane.

Now first inequality 4x  - 2y  < 5 .

-2y  < -4x + 5

y  > 2x - 5/2

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

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

Graph the boundary of the inequality y  > 2x - 5/2  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 4x - 2y < 5

0 < 5

The statement is true.

5) Since the statement is true , shade the region contain point (0,0),Shaded in maroon colour.

Now second inequality 5x + 2y > 3.

2y > -5x + 3

y > -5x /2 + 3/2

6) Graph the line y  = -5x /2 + 3/2

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

Graph the boundary of the inequality y > -5x /2 + 3/2  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 5x + 2y  > 3

0 > 3

The statement is false.

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

Now third inequality x + y < 4.

y < - x + 4

10) Graph the line y  = - x + 4

11) Since the inequality symbol is  <  the boundary is not included the solution set.

Graph the boundary of the inequality y < - x + 4  with dotted line.

12) 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 x + y < 4

0 < 4

The statement is true.

13) Since the statement is truese , shade the region contain point (0,0), shaded in green colour.

Graph :

The solution of the system is the set of ordered pairs in the intersection of the graph of

4x - 2y  < 5 , 5x + 2y  > 3 and x + y  < 4. This region is shaded in dark blue color.