12

-3

Step: 1

12x + 4y = -21

[Equation 1.]

Step: 2

-3x - y = 5

[Equation 2.]

Step: 3

[Revise equation 2.]

Step: 4

12x + 4(-3x - 5) = -21

[Substitute -3x - 5 for y in equation 1.]

Step: 5

20 ≠ 21

[Combine like terms.]

Step: 6

The variables are eliminated and the resulting statement is false.

Step: 7

So, the linear system has no solution.

Correct Answer is : No solution

Step: 1

5x + y = 3

[Equation 1.]

Step: 2

5x + y = 2

[Equation 2.]

Step: 3

[From Equation 2.]

Step: 4

5x + (- 5x + 2) = 3

[Substitute y = - 5x + 2 in Equation 1.]

Step: 5

2 = 3

[Combine like terms.]

Step: 6

The variables are eliminated and the resulting statement is false.

Step: 7

So, the linear system has no solution.

Correct Answer is : no solution

Step: 1

6x + y = 4

[Equation 1.]

Step: 2

6x + y = 3

[Equation 2.]

Step: 3

[From Equation 2.]

Step: 4

6x + (- 6x + 3) = 4

[Substitute y = - 6x + 3 in Equation 1.]

Step: 5

3 = 4

[Combine like terms.]

Step: 6

The variables are eliminated and the resulting statement is false.

Step: 7

So, the linear system has no solution.

Correct Answer is : no solution

Step: 1

9x + 3y = - 7

[Equation 1.]

Step: 2

- 3x - y = 2

[Equation 2.]

Step: 3

[Revise equation 2.]

Step: 4

9x + 3(- 3x - 2) = - 7

[Replace y with - 3x - 2 in Equation 1.]

Step: 5

9x - 9x - 6 = - 7

Step: 6

6 = 7

Step: 7

The variables are eliminated and the resulting statement is false.

Step: 8

So, the linear system has no solution.

Correct Answer is : no solution

Step: 1

4x + y = 29

[Equation 1.]

Step: 2

5x - 6y = 0

[Equation 2.]

Step: 3

[Rearrange Equation 1.]

Step: 4

5x - 6(- 4x + 29) = 0

[Replace y with - 4x + 29 in Equation 2.]

Step: 5

5x + 24x - 174 = 0

[Use distributive property.]

Step: 6

29x - 174 = 0

[Combine like terms.]

Step: 7

29x = 174

[Add 174 to both sides.]

Step: 8

[Solve for x .]

Step: 9

[Multiply.]

Step: 10

[Solve for y .]

Step: 11

So, the ordered pair (6, 5) is the solution for the linear system.

Step: 12

So, the linear system has exactly one solution.

Correct Answer is : exactly one solution

Step: 1

8x + y = 6

[Equation 1.]

Step: 2

8x + y = 7

[Equation 2.]

Step: 3

[From Equation 2.]

Step: 4

8x + (- 8x + 7) = 6

[Substitute the values.]

Step: 5

7 = 6

[Group the like terms.]

Step: 6

The variables are eliminated and the resulting statement, 7 = 6 is false.

Step: 7

So, the linear system has no solution.

Correct Answer is : Zero solutions

Step: 1

[Equation 1.]

Step: 2

[Equation 2.]

Step: 3

[From Equation 2.]

Step: 4

(3y + 4) - 3y = 7

[Replace x = 3y + 4 in Equation 1.]

Step: 5

4 = 7

[Combine like terms.]

Step: 6

The variables are eliminated and the resulting statement is false.

Step: 7

So, the linear system has no solution.

Correct Answer is : no solution

4

4

Step: 1

4x + y = 2

[Equation 1.]

Step: 2

4x + y = 1

[Equation 2.]

Step: 3

[From Equation 2.]

Step: 4

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

[Substitute y = - 4x + 1 in equation]

Step: 5

1 = 2

[Combine like terms.]

Step: 6

The variables are eliminated and the resulting statement is false.

Step: 7

So, the linear system has no solution.

Correct Answer is : no solution

Step: 1

10x + 5y = - 11

[Equation 1.]

Step: 2

- 2x - y = 2

[Equation 2.]

Step: 3

[Revise equation 2.]

Step: 4

10x + 5(- 2x - 2) = - 11

[Replace y with - 2x - 2 in Equation 1.]

Step: 5

10x - 10x - 10 = - 11

Step: 6

10 = 11

Step: 7

The variables are eliminated and the resulting statement is false.

Step: 8

So, the linear system has no solution.

Correct Answer is : no solution

Step: 1

- 8x + y = - 4

[Equation 1.]

Step: 2

160x - 20y = 80

[Equation 2.]

Step: 3

160x - 20y = 80

[Multiply Equation 1 by -20.]

Step: 4

The two equations are identical.

Step: 5

Any solution of 160x - 20y = 80 is also a solution of the system.

Step: 6

So, the linear system has infinitely many solutions.

Correct Answer is : infinitely many solutions

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