Step: 1

The graph of y < 4 is the half-plane below the dashed line y = 4

Step: 2

The graph of y > 3 2 x - 2 is the half-plane on and above the line y = 3 2 x - 2.

Step: 3

Graph both the inequalities in the same coordinate plane. The graph of the system is the overlap or intersection of the two half-planes shown as green color.

Correct Answer is : Graph 4

4

2

Step: 1

Write each equation in slope-intercept form y = mx + b , where m is the slope and b is the y -intercept.

Step: 2

4x + 2y = 3 ⇒ 2y = - 4x + 3 ⇒ y = ( - 2)x + 3 2 ----------- (1)

Step: 3

2y = x + 4 ⇒ y = (1 2 )x + 2 ------------ (2)

Step: 4

Graph the two equations using the slope and y -intercept.

Step: 5

Therefore, graph 1 represents the given system of linear equations.

Correct Answer is : Graph 1

2

Step: 1

Write each equation in slope-intercept form y = mx + b , where m is the slope and b is the y -intercept.

Step: 2

Step: 3

2x = 6(y + 1) ⇒ 6y = 2x - 6 ⇒ y = (1 3 )x - 1 -----------(2)

Step: 4

Graph the two equations using the slope and y -intercept.

Step: 5

Therefore, graph 2 represents the given system of linear equations.

Correct Answer is : Graph 2

2

6

Step: 1

Write each equation in slope-intercept form y = mx + b , where m is the slope and b is the y -intercept.

Step: 2

2x - 5y = 10 ⇒ 5y = 2x - 10 ⇒ y = (2 5 )x -2 ---------------(1)

Step: 3

6x = 15(y + 1) ⇒ 15y = 6x - 15 ⇒ y = (2 5 )x - 1 -----------------------(2)

Step: 4

Graph the two equations using the slope and y -intercept.

Step: 5

Therefore, graph 1 represents the given system of linear equations.

Correct Answer is : Graph 1

-5

6

Step: 1

Step: 2

- 5x + 6y = 8 ⇒ 6y = 5x + 8 ⇒ y = (5 6 )x + 4 3 -----------------------(1)

Step: 3

6x + 8y = 16 ⇒ 8y = - 6x + 16 ⇒ y = ( - 3 4 )x + 2 -------------------(2)

Step: 4

Graph the two equations using the slope and y -intercept.

Step: 5

Therefore, graph 1 represents the given system of linear equations.

Correct Answer is : Graph 1

3

- 9

Step: 1

Step: 2

3x - 2y = - 4 ⇒ 2y = 3x + 4 ⇒ y = (3 2 )x + 2 ---------------------(1)

Step: 3

- 9x + 6y = 12 ⇒ 6y = 9x + 12 ⇒ y = (3 2 )x + 2 ---------------------(2)

Step: 4

Graph the two equations using the slope and y -intercept.

Step: 5

Therefore, graph 4 represents the given system of linear equations.

Correct Answer is : Graph 4

6

9

Step: 1

Step: 2

6x - 2y = 4 ⇒ 2y = 6x - 4 ⇒ y = 3x - 2 ----------------(1)

Step: 3

9x - 3y = 3 ⇒ 3y = 9x - 3 ⇒ y = 3x - 1 -----------------(2)

Step: 4

Graph the two equations using the slope and y-intercept.

Step: 5

Therefore, graph 2 represents the given system of linear equations.

Correct Answer is : Graph 2

5x - 6y = 6

-3x + 2y = 2

Step: 1

Step: 2

5x - 6y = 6 ⇒ 6y = 5x - 6 ⇒ y = (5 6 )x - 1 -------------------(1)

Step: 3

- 3x + 2y = 2 ⇒ 2y = 3x + 2 ⇒ y = (3 2 )x + 1 ----------------------(2)

Step: 4

Graph the two equations using the slope and y -intercept.

Step: 5

Therefore, graph 4 represents the given system of linear equations.

Correct Answer is : Graph 4

3

4

Step: 1

Step: 2

3x + 5y = 15 ⇒ 5y = - 3x + 15 ⇒ y = ( - 3 5 )x + 3 ------------------------(1)

Step: 3

4x + 2y = 1 ⇒ 2y = - 4x + 1 ⇒ y = ( - 2)x + 1 2 -------------------------(2)

Step: 4

Graph the two equations using the slope and y - intercept.

Step: 5

Therefore, graph 4 represents the given system of linear equations.

Correct Answer is : Graph 4

Step: 1

The boundary of the half - plane is dashed if the inequality is < or > and solid if the inequality is ≤ or ≥.

Step: 2

The graph of x - y ≥ 2 is the half- plane below the Solid line x - y = 2.

Step: 3

The graph of x + y ≤ 0 is the half - plane below the solid line x + y = 0.

Step: 4

The graph of 2x - y > 1 is the half - plane above the dashed line 2x - y = 1

Step: 5

Graph all inequalities in the same coordinate plane. The graph of the system is the overlap, or intersection, of the three half-planes as shown below.

Correct Answer is : Graph 2

Step: 1

The boundary line of the half - plane is dashed if the inequality is < or > and solid if the inequality is ≤ or ≥.

Step: 2

The graph of 3x - 4y ≥ 4 is the half - plane below the solid line 3x - 4y = 4.

Step: 3

The graph of x + 2y > 0 is the half - plane above the dashed line x + 2y = 0

Step: 4

The graph of - 2x + 3y < 3 is the half - plane below the dashed line - 2x + 3y = 3.

Step: 5

Graph all inequalities in the same coordinate plane. The graph of the system is the overlap, or intersection, of the three half-planes as shown below.

Correct Answer is : Graph 1

Step: 1

The boundary line of the half-plane is dashed if the inequality is < or > and solid if the inequality is ≤ or ≥.

Step: 2

The graph of 3x + 4y ≤ 8 is the half - plane below the solid line 3x + 4y = 8

Step: 3

The graph of 2x - 3y < 9 is the half - plane above the dashed line 2x - 3y = 9

Step: 4

Graph the two inequalities in the same coordinate plane. The graph of the system is the overlap, or intersection, of the two half-planes as shown below.

Correct Answer is : Graph 1

Step: 1

The boundary line of the half-plane is dashed if the inequality is < or > and solid if the inequality is ≤ or ≥.

Step: 2

The graph of x > 2 is the half-plane to the right of the dashed line x = 2.

Step: 3

The graph of y ≤ - 3 is the half-plane below the solid line y = 3.

Step: 4

Graph the two inequalities in the same coordinate plane. The graph of the system is the overlap, or intersection, of the two half-planes as shown below.

Correct Answer is : Graph 2

Step: 1

|x - 1| ≤ 4

[First inequality.]

Step: 2

⇒ x - 1 ≤ 4 and x - 1 ≥ - 4

Step: 3

⇒ x ≤ 4 + 1 and x ≥ - 4 + 1 ⇒x ≤ 5 and x ≥ - 3

[Add 1 to both sides of the inequality.]

Step: 4

The graph of x ≤ 5 and x ≥ - 3 consists of the solid lines x = - 3 and x = 5 and the region between them.

Step: 5

|y + 2| ≥ 3

[Second inequality.]

Step: 6

⇒ y + 2 ≤ - 3 and y + 2 ≥ 3

Step: 7

⇒ y ≤ - 3 - 2 and y ≥ 3 - 2 ⇒ y ≤ - 5 and y ≥ 1

[Subtract 2 from both sides of the inequality.]

Step: 8

The graph of y ≤ - 5 and y ≥ 1 consists of all points on or above y = 1 and all points on or below y = - 5

Step: 9

Combine the two given inequalities. The solution of the given system includes all points on or above y = 1 between the solid lines x = - 3 and x = 5 and all points on or below y = - 5 between the solid lines x = - 3 and x = 5.

Correct Answer is : Graph 1

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- Coordinate Plane
- Graph
- System Of Inequalities