Math / Algebra

QuestionSystem B
Line 1: $y=3 x+3$
Line 2: $y=3 x$
This system of equations is: consistent dependent consistent independent inconsistent
This means the system has: a unique solution Solution: $\square$ $\square$ D) no solution infinitely many solutions

Studdy Solution

STEP 1

1. The problem involves analyzing a system of two linear equations.
2. We need to determine the relationship between the two lines represented by these equations.
3. The possible classifications for the system are consistent dependent, consistent independent, or inconsistent.
4. The possible outcomes for the system are a unique solution, no solution, or infinitely many solutions.

STEP 2

1. Compare the slopes of the two lines.
2. Compare the y-intercepts of the two lines.
3. Determine the classification of the system.
4. Determine the number of solutions based on the classification.

STEP 3

Compare the slopes of the two lines:
- For Line 1: $y = 3x + 3$ , the slope is $3$ . - For Line 2: $y = 3x$ , the slope is also $3$ .
Both lines have the same slope.

STEP 4

Compare the y-intercepts of the two lines:
- For Line 1: $y = 3x + 3$ , the y-intercept is $3$ . - For Line 2: $y = 3x$ , the y-intercept is $0$ .
The y-intercepts are different.

STEP 5

Determine the classification of the system:
- Since the slopes are the same and the y-intercepts are different, the lines are parallel and do not intersect.
This means the system is inconsistent.

STEP 6

Determine the number of solutions based on the classification:
- An inconsistent system has no solution.
The system is classified as inconsistent, which means it has no solution. Solution: $\boxed{\text{no solution}}$

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QuestionSystem B
Line 1: $y=3 x+3$
Line 2: $y=3 x$
This system of equations is: consistent dependent consistent independent inconsistent
This means the system has: a unique solution Solution: $\square$ $\square$ D) no solution infinitely many solutions

Studdy Solution

STEP 1

STEP 2

1. Compare the slopes of the two lines.
2. Compare the y-intercepts of the two lines.
3. Determine the classification of the system.
4. Determine the number of solutions based on the classification.

STEP 3

Compare the slopes of the two lines:
- For Line 1: $y = 3x + 3$ , the slope is $3$ . - For Line 2: $y = 3x$ , the slope is also $3$ .
Both lines have the same slope.

STEP 4

Compare the y-intercepts of the two lines:
- For Line 1: $y = 3x + 3$ , the y-intercept is $3$ . - For Line 2: $y = 3x$ , the y-intercept is $0$ .
The y-intercepts are different.

STEP 5

Determine the classification of the system:
- Since the slopes are the same and the y-intercepts are different, the lines are parallel and do not intersect.
This means the system is inconsistent.

STEP 6

Determine the number of solutions based on the classification:
- An inconsistent system has no solution.
The system is classified as inconsistent, which means it has no solution. Solution: $\boxed{\text{no solution}}$

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QuestionSystem BLine 1: y=3x+3y=3 x+3y=3x+3Line 2: y=3xy=3 xy=3xThis system of equations is: consistent dependent consistent independent inconsistentThis means the system has: a unique solution Solution: □\square□ □\square□ D) no solution infinitely many solutions

Studdy Solution

STEP 1

STEP 2

1. Compare the slopes of the two lines.2. Compare the y-intercepts of the two lines.3. Determine the classification of the system.4. Determine the number of solutions based on the classification.

STEP 3

Compare the slopes of the two lines:- For Line 1: y=3x+3 y = 3x + 3 y=3x+3, the slope is 3 3 3. - For Line 2: y=3x y = 3x y=3x, the slope is also 3 3 3.Both lines have the same slope.

STEP 4

Compare the y-intercepts of the two lines:- For Line 1: y=3x+3 y = 3x + 3 y=3x+3, the y-intercept is 3 3 3. - For Line 2: y=3x y = 3x y=3x, the y-intercept is 0 0 0.The y-intercepts are different.

STEP 5

Determine the classification of the system:- Since the slopes are the same and the y-intercepts are different, the lines are parallel and do not intersect.This means the system is inconsistent.

STEP 6

Determine the number of solutions based on the classification:- An inconsistent system has no solution. The system is classified as inconsistent, which means it has no solution. Solution: no solution\boxed{\text{no solution}}no solution​

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QuestionSystem B
Line 1: $y=3 x+3$
Line 2: $y=3 x$
This system of equations is: consistent dependent consistent independent inconsistent
This means the system has: a unique solution Solution: $\square$ $\square$ D) no solution infinitely many solutions

1. Compare the slopes of the two lines.
2. Compare the y-intercepts of the two lines.
3. Determine the classification of the system.
4. Determine the number of solutions based on the classification.

Compare the slopes of the two lines:
- For Line 1: $y = 3x + 3$ , the slope is $3$ . - For Line 2: $y = 3x$ , the slope is also $3$ .
Both lines have the same slope.

Compare the y-intercepts of the two lines:
- For Line 1: $y = 3x + 3$ , the y-intercept is $3$ . - For Line 2: $y = 3x$ , the y-intercept is $0$ .
The y-intercepts are different.

Determine the classification of the system:
- Since the slopes are the same and the y-intercepts are different, the lines are parallel and do not intersect.
This means the system is inconsistent.

Determine the number of solutions based on the classification:
- An inconsistent system has no solution.
The system is classified as inconsistent, which means it has no solution. Solution: $\boxed{\text{no solution}}$