Podcast
Questions and Answers
What can be concluded if two equations have the same slope but different y-intercepts?
What can be concluded if two equations have the same slope but different y-intercepts?
- There is one solution to the system.
- The system has no solution. (correct)
- The equations are identical.
- The system has infinitely many solutions.
What is the solution type for the system of equations y = 2x + 2 and -6x + 4y = 2?
What is the solution type for the system of equations y = 2x + 2 and -6x + 4y = 2?
- Infinitely many solutions (correct)
- No solution
- One solution
- Undefined solution
Which pair of equations results in exactly one solution?
Which pair of equations results in exactly one solution?
- 7x + 3y = 10 and 7x + 3y = 30
- y = 1.5x + 9 and y = 1.5x - 9
- y = 2x + 2 and y = 2x + 5
- y = x + 1 and y = -x - 1 (correct)
Identifying the correct reasoning, what is true for the equations 7x + 3y = 10 and 7x + 3y = 30?
Identifying the correct reasoning, what is true for the equations 7x + 3y = 10 and 7x + 3y = 30?
What condition results in a system of equations having infinitely many solutions?
What condition results in a system of equations having infinitely many solutions?
Flashcards
No Solution System
No Solution System
A system of equations with the same slope but different y-intercepts has no solution.
Infinitely Many Solutions System
Infinitely Many Solutions System
A system of equations with the same slope and the same y-intercept has infinitely many solutions.
Solving by Inspection
Solving by Inspection
To solve a system of equations by inspection, you need to compare the slopes and y-intercepts of the equations.
One Solution System
One Solution System
Signup and view all the flashcards
Identifying Solutions by Inspection
Identifying Solutions by Inspection
Signup and view all the flashcards
Study Notes
Solving Systems by Inspection
- Systems of equations can be solved by inspection, observing the equations instead of using a full algebraic method.
- If two equations have the same slope but different y-intercepts, the system has no solution.
- If two equations have the same slope and the same y-intercept, the system has infinite solutions.
Examples
-
Problem 1:
- y = 1.5x + 9
- y = 1.5x – 9
- Solution: No solution (same slope, different y-intercepts)
-
Problem 2:
- 7x + 3y = 10
- 7x + 3y = 30
- Solution: No solution (same slope, different y-intercepts)
-
Problem 3:
- y = x + 1
- y = –x – 1
- Solution: One solution
-
Problem 4:
- y = 2x + 2
- –8x + 4y = 2
- Solution: Infinite solutions (same slope, same y-intercept after simplifying equations)
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
