Step: 1

The two lines appear to intersect at the point (1, - 2).

Step: 2

Check the solution algebraically:y + x + 1 = 0

[Equation 1.]

Step: 3

(- 2) + 1 + 1 = 0

[Substitute x = 1 and y = - 2 in equation 1.]

Step: 4

0 = 0

[Simplify.]

Step: 5

[Equation 2.]

Step: 6

- 2 + 3(1) - 1 = 0

[Substitute x = 1 and y = - 2 in equation 2.]

Step: 7

0 = 0

[Simplify.]

Step: 8

The ordered pair (1, - 2) satisfies both the equations.

Step: 9

So, (1, - 2) is the solution of the linear system.

Correct Answer is : (1, - 2)

Step: 1

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

Step: 2

- 10x + 5y = - 20 ----(2)

Step: 3

Dividing Equation (2) by 5, we get - 2x + y = - 4

Step: 4

Graph the equations.

Step: 5

Both the equations represent the same line. So, each point on the line is a solution of the system.

Step: 6

So, the pair of equations has infinitely many solutions.

Correct Answer is : Infinitely many solutions

Step: 1

From the graph, the y - intercept of the line A is -3.

Step: 2

Slope of the line A = - 3 - ( - 5 ) 0 - 3 = - 2 3

[Line A passes through (0, -3) and (3, -5)]

Step: 3

The equation of the line A is y = ( - 2 3 )x + ( - 3) ⇒ 2x + 3y = - 9.

[Slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.]

Step: 4

From the graph, the y - intercept of the line B is - 1.

Step: 5

Slope of the line B = - 1 - ( - 5 ) 0 - 3 = - 4 3

[Line B passes through (0, - 1) and (3, -5)]

Step: 6

The equation of the line B is y = ( -4 3 ) x + (- 1) ⇒ 4x + 3y = - 3.

[Slope-intercept form of a line is y = mx + b , where m is the slope and b is the y -intercept.]

Step: 7

Therefore, the linear system represented by the graph is 2x + 3y = - 9, 4x +3y = - 3.

Correct Answer is : 2x + 3y = -9, 4x + 3y = - 3

2

Step: 1

The graphs represented by the given system of equations appear to intersect at (-6, 0). Therefore, the solution is (-6, 0).

Step: 2

Check the solution algebraically by substituting x = - 6 and y = 0 in each of the equations.

Step: 3

2x - 3y = - 12 ⇒ 2(- 6) - 3(0) = - 12 ⇒ - 12 = - 12

[Substitute x = - 6 and y = 0 in equation 1 and then simplify.]

Step: 4

[Substitute x = - 6 and y = 0 in equation 2 and then simplify.]

Step: 5

The ordered pair (-6, 0) satisfies both the equations. Hence, (-6, 0) is the solution of the given linear system.

Correct Answer is : (-6, 0)

2

Step: 1

The graphs represented by the given system of equations appear to intersect at (6, 5). Therefore, the solution is (6, 5).

Step: 2

Check the solution algebraically by substituting x = 6 and y = 5 in each of the equations.

Step: 3

[Substitute x = 6 and y = 5 in equation 1 and then simplify.]

Step: 4

2x - 3y = - 3 ⇒ 2(6) - 3(5) = - 3 ⇒ - 3 = - 3

[Substitute x = 6 and y = 5 in equation 2 and then simplify.]

Step: 5

The ordered pair (6, 5) satisfies both the equations. Hence, (6, 5) is the solution of the given linear system.

Correct Answer is : (6, 5)

Step: 1

From the graph, the y - intercept of the line A is -4.

Step: 2

Slope of the line A = - 4 - 2 0 - 2 = 3

[Line A passes through (0, - 4) and (2, 2)]

Step: 3

The equation of the line A is y = 3x + ( - 4) ⇒ 3x - y = 4.

[Slope-intercept form of a line is y = mx + b , where m is the slope and b is the y -intercept.]

Step: 4

From the graph, the y - intercept of the line B is 3.

Step: 5

Slope of the line B = 3 - 2 0 - 2 = - 1 2

[Line B passes through (0, 3) and (2, 2)]

Step: 6

The equation of the line B is y = (- 1 2 ) x + 3 ⇒ x + 2y = 6.

[Slope-intercept form of a line is y = mx + b , where m is the slope and b is the y -intercept.]

Step: 7

Therefore, the linear system represented by the graph is 3x - y = 4, x + 2y = 6.

Correct Answer is : 3x - y = 4, x + 2y = 6

3

Step: 1

The graphs represented by the given system of equations appear to intersect at (3, - 5 2 ). Therefore, the solution is (3, - 5 2 ).

Step: 2

Check the solution algebraically by substituting x = 3 and y = - 5 2 in each of the equation.

Step: 3

[substitute x = 3 and y = - 5 2 in equation 1 and then simplify.]

Step: 4

3x + 2y = 4 ⇒ 3(3) + 2(- 5 2 ) = 4 ⇒ 4 = 4

[Substitute x = 3 and y = - 5 2 in equation 2 and then simplify.]

Step: 5

The ordered pair (3, - 5 2 ) satisfies both the equations. Hence, (3, - 5 2 ) is the solution of the given linear system.

Correct Answer is : (3, - 5 2 )

2

Step: 1

The graphs represented by the given system of equations appear to intersect at (2, 1). Therefore, the solution is (2, 1).

Step: 2

Check the solution algebraically by substituting x = 2 and y = 1 in each of the equations.

Step: 3

2x - y = 3 ⇒ 2(2) - 1 = 3 ⇒ 3 = 3

[Substitute x = 2 and y = 1 in equation 1 and then simplify.]

Step: 4

[Substitute x = 2 and y = 1 in equation 2 and then simplify.]

Step: 5

The ordered pair (2, 1) satisfies both the equation. Hence, (2, 1) is the solution of the given linear system.

Correct Answer is : (2, 1)

2

2

Step: 1

The graphs represented by the given system of equations appear to intersect at (3 2 , 0). Therefore, the solution is (3 2 , 0).

Step: 2

Check the solution algebraically by substituting x = 3 2 and y = 0 in each of the equation.

Step: 3

2x - y = 3 ⇒ 2(3 2 ) - 0 = 3 ⇒ 3 = 3

[Substitute x = 3 2 and y = 0 in equation 1 and then simplify.]

Step: 4

2x + 3y = 3 ⇒ 2(3 2 ) + 3(0) = 3 ⇒ 3 = 3

[Substitute x = 3 2 and y = 0 in equation 2 and then simplify.]

Step: 5

The ordered pair (3 2 , 0) satisfies both the equation. Hence, (3 2 , 0) is the solution of the given linear system.

Correct Answer is : (3 2 , 0)

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