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?
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?
Which pair of equations results in exactly one solution?
Which pair of equations results in exactly one solution?
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?
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What condition results in a system of equations having infinitely many solutions?
What condition results in a system of equations having infinitely many solutions?
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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
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Problem 1:
- y = 1.5x + 9
- y = 1.5x – 9
- Solution: No solution (same slope, different y-intercepts)
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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)
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Description
This quiz covers the method of solving systems of equations by inspection. It highlights the conditions for having no solution, one solution, or infinite solutions based on the slopes and y-intercepts of the equations. Test your understanding of these concepts through provided examples.
