Step: 1

[Equation 1.]

Step: 2

[Equation 2.]

Step: 3

Graph both the equations using slope and y -intercept.

Step: 4

The two equations have different slopes.

Step: 5

It can be observed that both the lines intersect at only one point.

Step: 6

So, the linear system has exactly one solution.

Correct Answer is : Exactly one solution

Step: 1

The equation of the line in slope-intercept form with slope m and y -intercept b is y = mx + b .

Step: 2

From the graph, y -intercept of line A is 0 and slope is 2 3 .

Step: 3

The equation of the line A is y = 2 3 x .

[Substitute slope = 2 3 and y -intercept = 0 in the slope-intercept form equation.]

Step: 4

3y = 2x

[Simplify.]

Step: 5

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

Step: 6

The equation of the line B is y = x - 1.

[Substitute slope = 1 and y -intercept = - 1 in the slope-intercept form equation.]

Step: 7

The linear system is

3y = 2x

y = x - 1.

3

Correct Answer is : 3y = 2x , y = x - 1

Step: 1

[Equation 1.]

Step: 2

[Equation 2.]

Step: 3

Graph the equations.

Step: 4

The lines are intersecting at a point (5, 8).

Step: 5

So, there is only one solution (5, 8).

Step: 6

Therefore, the system is consistent and independent.

Correct Answer is : consistent and independent

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

[Equation 1.]

Step: 2

[Equation 2.]

Step: 3

Graph the equations.

Step: 4

It appears that the two lines intersect at the point (4, 4).

[From graph.]

Step: 5

Check the solution algebraically :

Step: 6

[Equation 1.]

Step: 7

4 = 4, which is true.

[Substitute x = 4 and y = 4.]

Step: 8

[Equation 2.]

Step: 9

4 = 4, which is true.

[Substitute y = 4.]

Step: 10

So, (4, 4) is the solution of the linear system.

Correct Answer is : (4, 4)

Step: 1

[Original system of equations.]

Step: 2

Graph the given equaions.

Step: 3

The graphical solution is (- 1, - 1).

Step: 4

Check the solution by substitution:

Use - 1 forx in equation (1).

Use - 1 for

Step: 5

[Substitute the values.]

Step: 6

[Multiply and add.]

Step: 7

The exact solution is (- 1, - 1), which is same as graphical solution.

Correct Answer is : (- 1, - 1)

Step: 1

[Equation 1.]

Step: 2

[Equation 2.]

Step: 3

Graph the equations.

Step: 4

It appears that the two lines intersect at the point (4, - 4).

[From graph.]

Step: 5

Check the solution algebraically :

Step: 6

[Equation 1.]

Step: 7

- 4 = - 4, which is true.

[Substitute x = 4 and y = - 4.]

Step: 8

[Equation 2.]

Step: 9

4 = 4, which is true.

[Substitute x = 4.]

Step: 10

So, (4, - 4) is the solution of the linear system.

Correct Answer is : (4, - 4)

Step: 1

[Equation 1.]

Step: 2

[Equation 2.]

Step: 3

Graph the equations.

Step: 4

It appears that the two lines intersect at the point (- 2, - 4).

[From graph.]

Step: 5

Check the solution algebraically :

Step: 6

[Equation 1.]

Step: 7

- 4 = - 4, which is true.

[Substitute x = - 2 and y = - 4.]

Step: 8

[Equation 2.]

Step: 9

- 4 = - 4, which is true.

[Substitute y = - 4.]

Step: 10

So, (- 2, - 4) is the solution of the linear system.

Correct Answer is : (- 2, - 4)

2

Step: 1

Let us draw the graphs of the Equations (1) and (2). For this, we find two
solutions of each of the equations, which are given in Tables.

Step: 2

Plot the points A(- 1, 3), B(0, 1), P(- 1, 3) and Q(0, 2) on graph paper, and join the points to form the lines AB and PQ as shown in Figure.

Step: 3

We observe that there is a point B (- 1, 3) common to both the lines AB and PQ. So, the solution of the pair of linear equations is x = - 1 and y = 3.

Correct Answer is : Graph 1

3

Step: 1

3y = 2x

y = x - 1

[Given simultaneous linear equations.]

Step: 2

3y = 2x ⇒ y = 2 3 x

Step: 3

When x = - 3, y = 2 3 (- 3) = - 2

Whenx = 0, y = 2 3 (0) = 0

Whenx = 3, y = 2 3 (3) = 2

When

When

Step: 4

Thus, we get the following table:

Step: 5

Step: 6

When x = - 1, y = - 1 - 1 = - 2

Whenx = 0, y = 0 - 1 = - 1

Whenx = 3, y = 3 - 1 = 2.

When

When

Step: 7

Thus, we get the following table:

Step: 8

Plot the points on a graph paper.

Step: 9

From the graph, the two lines intersect at (3, 2).

Step: 10

So, the solution for the given simultaneous linear equations is (3, 2).

Correct Answer is : (3, 2)

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