Podcast
Questions and Answers
What are the two equations that could determine how many children's and adult's tickets were sold?
What are the two equations that could determine how many children's and adult's tickets were sold?
6X + 2Y = 750, X + Y = 175
What are the two numbers if their sum is 45 and their difference is 21?
What are the two numbers if their sum is 45 and their difference is 21?
(33, 12)
Coinciding lines have _____________ solutions.
Coinciding lines have _____________ solutions.
infinitely many
Parallel lines have _______________ solutions.
Parallel lines have _______________ solutions.
Intersecting lines have _______________ solution.
Intersecting lines have _______________ solution.
The first step for substitution is you either solve for ___________ or ___________.
The first step for substitution is you either solve for ___________ or ___________.
What is the solution of the two equations: A. Y = -8X -10 B. -8X - Y = 10?
What is the solution of the two equations: A. Y = -8X -10 B. -8X - Y = 10?
What is the solution for the system of equations: A. 3X + Y = -5 B. X = -2?
What is the solution for the system of equations: A. 3X + Y = -5 B. X = -2?
What is the solution for the system of equations: A. X + 2Y = 8 B. Y = -X +7?
What is the solution for the system of equations: A. X + 2Y = 8 B. Y = -X +7?
The standard form is always _______________ and no __________________.
The standard form is always _______________ and no __________________.
What is the solution using elimination for the equations: A. 3X - 4Y= -2 B. 6X - 8Y = -4?
What is the solution using elimination for the equations: A. 3X - 4Y= -2 B. 6X - 8Y = -4?
What is the solution using elimination: A. Y = 3X -12 B. Y= -2X + 3?
What is the solution using elimination: A. Y = 3X -12 B. Y= -2X + 3?
Solutions are where the shading __________________.
Solutions are where the shading __________________.
Dashed lines indicate: < LESS THAN > GREATER THAN
Dashed lines indicate: < LESS THAN > GREATER THAN
Solid lines indicate: < LESS THAN OR EQUAL TO, > GREATER THAN OR EQUAL TO
Solid lines indicate: < LESS THAN OR EQUAL TO, > GREATER THAN OR EQUAL TO
Shade above for: > GREATER THAN, GREATER THAN OR EQUAL TO
Shade above for: > GREATER THAN, GREATER THAN OR EQUAL TO
Shade below for: < LESS THAN, LESS THAN OR EQUAL TO
Shade below for: < LESS THAN, LESS THAN OR EQUAL TO
What are the possible solutions for: A. Y < 1/2X +1 B. Y (GREATER THAN OR EQUAL TO) -3X -1?
What are the possible solutions for: A. Y < 1/2X +1 B. Y (GREATER THAN OR EQUAL TO) -3X -1?
What are the steps for creating systems of equations?
What are the steps for creating systems of equations?
What are the equations to determine the individual price of shorts and sunglasses?
What are the equations to determine the individual price of shorts and sunglasses?
Write a system of linear equations to determine two numbers if twice a number added to another is 18 and four times the first number minus the other is 12.
Write a system of linear equations to determine two numbers if twice a number added to another is 18 and four times the first number minus the other is 12.
What are the equations to determine how many dimes are in a jar filled with nickels and dimes?
What are the equations to determine how many dimes are in a jar filled with nickels and dimes?
What are the steps for solving systems by graphing?
What are the steps for solving systems by graphing?
Intersecting lines have ____________ solutions.
Intersecting lines have ____________ solutions.
Parallel lines have ____________ solutions.
Parallel lines have ____________ solutions.
Coinciding lines have ____________ solutions.
Coinciding lines have ____________ solutions.
What is the slope of the line Y = -4X + 5?
What is the slope of the line Y = -4X + 5?
What is the Y-intercept of Y = 2X -6?
What is the Y-intercept of Y = 2X -6?
Write the equation Y - 3X = 5 in slope-intercept form.
Write the equation Y - 3X = 5 in slope-intercept form.
What is 5X + Y = -2 written in slope-intercept form?
What is 5X + Y = -2 written in slope-intercept form?
What is the slope of the line -6X + 2Y = 3?
What is the slope of the line -6X + 2Y = 3?
What is the slope of the line 4X - 2Y = 8?
What is the slope of the line 4X - 2Y = 8?
What is Y + X = 3 in slope-intercept form?
What is Y + X = 3 in slope-intercept form?
What type of function has a straight line graph?
What type of function has a straight line graph?
What is the slope of two parallel lines?
What is the slope of two parallel lines?
Which is a method of solving systems of equations?
Which is a method of solving systems of equations?
Which method would be best used to solve the system: Y = -2X + 8, Y = X + 3?
Which method would be best used to solve the system: Y = -2X + 8, Y = X + 3?
Which method would be best used to solve the system: Y = 4X + 8, X = 3?
Which method would be best used to solve the system: Y = 4X + 8, X = 3?
Which method would be best used to solve the system: 3X - 2Y = 8, 5X + 2Y = 3?
Which method would be best used to solve the system: 3X - 2Y = 8, 5X + 2Y = 3?
Which method would be best used to solve the system: 4X - 8Y = 8, 5X + 2Y = 3?
Which method would be best used to solve the system: 4X - 8Y = 8, 5X + 2Y = 3?
What is the value of X to the solution: 4X - 2Y = 8, 5X + 2Y = 10?
What is the value of X to the solution: 4X - 2Y = 8, 5X + 2Y = 10?
What is the value of Y to the solution: 3X - 2Y = 2, -3X + 5Y = -8?
What is the value of Y to the solution: 3X - 2Y = 2, -3X + 5Y = -8?
What is the value of X to the solution: 3X - 2Y - 2, Y = 11?
What is the value of X to the solution: 3X - 2Y - 2, Y = 11?
What is the value of Y to the solution: X + 5Y = 14, X = Y + 2?
What is the value of Y to the solution: X + 5Y = 14, X = Y + 2?
What is the solution to this system of linear equations: X + 5Y =18, X=3?
What is the solution to this system of linear equations: X + 5Y =18, X=3?
What is the solution to this system of linear equations: 2X + Y = 18, Y = 3X -2?
What is the solution to this system of linear equations: 2X + Y = 18, Y = 3X -2?
What is the solution to this system of linear equations: 2X + Y = 2, -2X - 3Y= 10?
What is the solution to this system of linear equations: 2X + Y = 2, -2X - 3Y= 10?
What is the solution to this system of linear equations: 2X + Y = 3, -X - Y = -1?
What is the solution to this system of linear equations: 2X + Y = 3, -X - Y = -1?
What is the solution to this system of linear equations: 3X + 4Y = 3, -X - 5Y = 10?
What is the solution to this system of linear equations: 3X + 4Y = 3, -X - 5Y = 10?
Flashcards
Systems of Equations
Systems of Equations
Two or more equations with the same variables.
Adult and Child Tickets Example
Adult and Child Tickets Example
A problem involving ticket sales yielding two equations: 6X + 2Y = 750 and X + Y = 175.
Solution to Ticket Problem
Solution to Ticket Problem
The solution (100, 75) represents adults and children's tickets sold.
Sum and Difference
Sum and Difference
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Solution for Sum and Difference
Solution for Sum and Difference
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Coinciding Lines
Coinciding Lines
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Parallel Lines
Parallel Lines
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Intersecting Lines
Intersecting Lines
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Substitution Method
Substitution Method
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Elimination Method
Elimination Method
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Types of Solutions
Types of Solutions
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Graphing Inequalities
Graphing Inequalities
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Slope-Intercept Form
Slope-Intercept Form
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Finding Slope
Finding Slope
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Finding Y-intercept
Finding Y-intercept
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Linear Functions
Linear Functions
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Slope of Parallel Lines
Slope of Parallel Lines
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Solving by Substitution
Solving by Substitution
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System Verification Example
System Verification Example
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Multiple Systems Solutions
Multiple Systems Solutions
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Inequalities Shading Rules
Inequalities Shading Rules
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Identifying Infinitely Many Solutions
Identifying Infinitely Many Solutions
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Mastering Systems of Equations
Mastering Systems of Equations
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Modeling Real-world Scenarios
Modeling Real-world Scenarios
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Study Notes
Systems of Equations
- Movie ticket prices: $6 for adults, $2 for children; total tickets sold = 175, total cash = $750.
- System of equations:
- 6X + 2Y = 750
- X + Y = 175
- Solution for adult and children's tickets: (100, 75).
Solving for Numbers
- The sum of two numbers is 45, and their difference is 21.
- System of equations:
- X + Y = 45
- X - Y = 21
- Solution: (33, 12).
Lines and Solutions
- Coinciding lines have infinitely many solutions (same line).
- Parallel lines have no solutions (do not intersect).
- Intersecting lines have one solution (unique intersection point).
Substitution Method
- First step in substitution: solve for X or Y.
Elimination Method
- Eliminating variables can lead to:
- Infinitely many solutions
- No solution
- A unique solution
- Example solution using elimination: from equations 3X - 4Y = -2 and 6X - 8Y = -4 leads to infinitely many solutions.
Inequalities and Graphing
- Systems of inequalities must be in slope-intercept form.
- Graph with solid/dashed lines and shade above or below.
- Solutions are where shading overlaps; points on solid lines are solutions, points on dashed lines are not.
Slope and Intercepts
- Slope of line Y = -4X + 5 is -4.
- Y-intercept of line Y = 2X - 6 is -6.
- Slope-intercept form is Y = mx + b.
Types of Functions
- Linear functions produce straight line graphs.
- Slope of parallel lines is the same.
- Various methods for solving systems: graphing, substitution, elimination.
Solving Specific Systems
- Use substitution or elimination based on the situation.
- Example: Y = -2X + 8 and Y = X + 3 solved by substitution.
System Solutions
- Solutions can be found for various equations such as:
- X + 5Y = 18, X = 3 gives (3, 3).
- 2X + Y = 18, Y = 3X - 2 gives (4, 10).
- Systems can also yield various values of X and Y depending on the setup.
Conclusion
- Mastery of systems of equations, inequalities, and their respective solutions is essential in algebra.
- Equations can model real-world scenarios effectively through structured methods like substitution and elimination.
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Description
Test your knowledge with this Algebra 1 Unit 6 quiz focused on systems of equations. Solve practical problems involving adult and children's movie ticket sales, and learn to set up and solve simultaneous equations. This quiz is designed to enhance your algebraic problem-solving skills.
