Podcast
Questions and Answers
What is the defining characteristic of a 'system of linear equations'?
What is the defining characteristic of a 'system of linear equations'?
- It strictly involves quadratic equations.
- It involves only one equation.
- It only applies to geometric problems.
- It is defined by two or more equations considered together. (correct)
A solution to a system of two equations must satisfy only one of the equations.
A solution to a system of two equations must satisfy only one of the equations.
False (B)
If a system of equations represents the number of eyes and feet of flamingos and zebras, and f represents flamingos while z represents zebras, what does the equation 2f + 4z = 44 represent?
If a system of equations represents the number of eyes and feet of flamingos and zebras, and f represents flamingos while z represents zebras, what does the equation 2f + 4z = 44 represent?
the total number of feet
In the context of solving systems of equations graphically, the solution is represented by the __________ of two lines.
In the context of solving systems of equations graphically, the solution is represented by the __________ of two lines.
A school district wants to model the number of small buses (s) and large buses (l). If small buses carry 12 passengers and large buses carry 24, and the total capacity is 780, which equation correctly models this?
A school district wants to model the number of small buses (s) and large buses (l). If small buses carry 12 passengers and large buses carry 24, and the total capacity is 780, which equation correctly models this?
If two lines in a system of equations are parallel, the system has one unique solution.
If two lines in a system of equations are parallel, the system has one unique solution.
What condition must be met to verify if a given point (x, y) is a solution to a given system of equations?
What condition must be met to verify if a given point (x, y) is a solution to a given system of equations?
When solving a system of equations graphically using a calculator, the intersection point is found using the __________ function.
When solving a system of equations graphically using a calculator, the intersection point is found using the __________ function.
Which statement is true regarding a system of equations that has infinite solutions?
Which statement is true regarding a system of equations that has infinite solutions?
In the elimination method, you must always add the equations together; subtraction is not an option.
In the elimination method, you must always add the equations together; subtraction is not an option.
If a hotdog (h) costs $x and a drink (d) costs $y, write a system of equations representing '3 hotdogs and 5 drinks cost $21' and '6 hotdogs and 4 drinks cost $24'.
If a hotdog (h) costs $x and a drink (d) costs $y, write a system of equations representing '3 hotdogs and 5 drinks cost $21' and '6 hotdogs and 4 drinks cost $24'.
A linear system where the graphs of the two equations are parallel lines is called __________.
A linear system where the graphs of the two equations are parallel lines is called __________.
What does it mean graphically if a linear system of equations is classified as 'dependent'?
What does it mean graphically if a linear system of equations is classified as 'dependent'?
When using substitution, you must solve for 'x' in terms of 'y'; solving for 'y' in terms of 'x' is incorrect.
When using substitution, you must solve for 'x' in terms of 'y'; solving for 'y' in terms of 'x' is incorrect.
To determine if two linear equations have one solution, no solution, or infinitely many solutions, what should you compare after converting them to slope-intercept form?
To determine if two linear equations have one solution, no solution, or infinitely many solutions, what should you compare after converting them to slope-intercept form?
In the context of linear systems, if all the points that satisfy one equation also satisfy the other equation, the system has __________ many solutions.
In the context of linear systems, if all the points that satisfy one equation also satisfy the other equation, the system has __________ many solutions.
Match the following system characteristics with their corresponding number of solutions:
Match the following system characteristics with their corresponding number of solutions:
Given a system of equations where one equation is $y = -3x + 5$, which of the following equations would result in a system with no solution?
Given a system of equations where one equation is $y = -3x + 5$, which of the following equations would result in a system with no solution?
Explain why a system of linear equations that, when solved using elimination, results in the equation $0 = -3$ has no solution?
Explain why a system of linear equations that, when solved using elimination, results in the equation $0 = -3$ has no solution?
A system of linear equations that results in an identity (e.g., 0 = 0) after applying the elimination method indicates that the system has __________ many solutions.
A system of linear equations that results in an identity (e.g., 0 = 0) after applying the elimination method indicates that the system has __________ many solutions.
Flashcards
System of Linear Equations
System of Linear Equations
Two equations that are considered together.
System of Equations
System of Equations
A set of equations that are considered together.
Solution to a System of Two Equations
Solution to a System of Two Equations
A pair of values that satisfy both equations in a system.
Solving a Linear System of Equations
Solving a Linear System of Equations
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One Solution
One Solution
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No Solution
No Solution
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Infinitely Many Solutions
Infinitely Many Solutions
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Substitution Method
Substitution Method
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Elimination Method
Elimination Method
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Study Notes
- A system of linear equations consists of two equations.
- An equation system model can verify answers.
System of Equations
- A system of equations is a set of equations considered together.
- A solution to a system of two equations is a pair of values that satisfy both equations.
Solving Linear Equations Graphically (Manually)
- A pair of equations considered together comprises a system of equations.
- Solving a system of equations is determining the values that satisfy both equations.
- The solution is the intersection point (ordered pair) lying on both graphs.
Solving Linear Equations Graphically on the TI-83/84
- Rearrange equations into slope-intercept form
- Input two equations in "y="
- Press 2nd, then Calc, then intersect.
- Follow prompts using the Enter button.
Solving Linear Equations Algebraically by Substitution
- The substitution method algebraically solves a system of equations in terms of x or y.
- Steps:
- Isolate one variable by rearranging the equation.
- Substitute the expression into the other equation.
- Solve for the single variable.
- Substitute the value back into either original equation to solve for the other variable.
- Write the solution as an ordered pair.
- Verify the solution in both original equations.
Solving a Linear System by Adding or Subtracting Equations
- Write the equations in standard form (Ax + By = C)
- Multiply one or both by a constant so the coefficients are different by their sign
- Add / subtract, solving for one of the variables
- Substitute to find the other variable
- Check the solution
Properties of Systems of Linear Equations
- Systems of equations can have no solutions, one solution, or infinite solutions.
- One Solution: The lines intersect at one point, with different slopes and y-intercepts. This is a consistent, independent system.
- No Solution: The lines are parallel with the same slope, but the y-intercepts can be different. This is an inconsistent system.
- Infinite Solutions: The equations produce the same line with the same slope and y-intercept. This is a consistent, dependent system.
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