Podcast
Questions and Answers
What is the solution to a system of equations represented by two intersecting lines on a graph?
What is the solution to a system of equations represented by two intersecting lines on a graph?
- No solution
- Infinitely many solutions
- Two points
- A single point (correct)
If two lines in a system of equations are parallel, there is at least one solution.
If two lines in a system of equations are parallel, there is at least one solution.
False (B)
What would you do first when using the elimination method on a system of equations?
What would you do first when using the elimination method on a system of equations?
Arrange the equations in standard form.
To graph a linear inequality, you first graph the corresponding linear __________.
To graph a linear inequality, you first graph the corresponding linear __________.
Match the methods of solving systems of equations with their descriptions:
Match the methods of solving systems of equations with their descriptions:
Flashcards
What is the solution to a system of equations?
What is the solution to a system of equations?
The solution to a system of equations is the point where the graphs of the equations intersect. This point represents the values of the variables that satisfy both equations simultaneously.
Parallel Lines in System
Parallel Lines in System
If the graphs of a system of equations are parallel lines, the system has no solution. Parallel lines never intersect, so there is no point that satisfies both equations.
Substitution Method
Substitution Method
The substitution method involves solving one equation for one variable and substituting that expression into the other equation to solve for the remaining variable.
Elimination Method
Elimination Method
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Linear Inequality Graphing
Linear Inequality Graphing
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Study Notes
Solving Systems of Equations by Graphing
- Graph both equations on the same coordinate plane.
- The point where the lines intersect is the solution to the system.
- If the lines are parallel, the system has no solution.
- If the lines are the same, the system has infinitely many solutions.
Solving Systems of Equations by Substitution
- Solve one equation for one variable.
- Substitute the expression into the other equation.
- Solve for the remaining variable.
- Substitute the value back into the first equation to find the other variable.
Solving Systems of Equations by Elimination
- Arrange equations in standard form (Ax + By = C).
- Multiply one or both equations by constants to make the coefficients of one variable opposites.
- Add the equations to eliminate one variable.
- Solve for the remaining variable.
- Substitute the value back into either original equation to find the other variable.
Linear Inequalities in Two Variables
- A linear inequality in two variables can be written in the form Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C.
- The solution to a linear inequality in two variables is a half-plane.
- To graph a linear inequality, first graph the corresponding linear equation.
- Use a dashed line for < or >, and a solid line for ≤ or ≥.
- Test a point not on the line to determine which half-plane to shade.
Systems of Linear Inequalities
- A system of linear inequalities in two variables consists of two or more linear inequalities.
- The solution to a system of linear inequalities is the intersection of the solution sets of the individual inequalities.
- Graph each inequality on the same coordinate plane.
- The overlapping shaded region is the solution to the system.
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Description
This quiz covers various methods for solving systems of equations, including graphing, substitution, and elimination. Additionally, it explores linear inequalities in two variables. Test your understanding of these fundamental algebra concepts.
