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Questions and Answers
What is the highest power of the variable(s) in a linear equation?
What is the highest power of the variable(s) in a linear equation?
What is the slope-intercept form of a linear equation?
What is the slope-intercept form of a linear equation?
What is the graphical method used for?
What is the graphical method used for?
What is the purpose of the addition and subtraction method in solving linear equations?
What is the purpose of the addition and subtraction method in solving linear equations?
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What type of linear equation has only one variable?
What type of linear equation has only one variable?
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What is the elimination method used for?
What is the elimination method used for?
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What does the y-intercept of a line represent?
What does the y-intercept of a line represent?
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What is a system of linear equations?
What is a system of linear equations?
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Study Notes
Definition and Notation
- A linear equation is an equation in which the highest power of the variable(s) is 1.
- Linear equations can be written in the form: ax + by = c, where a, b, and c are constants, and x and y are variables.
Types of Linear Equations
- Simple Linear Equations: Equations with only one variable, e.g. 2x = 5.
- Linear Equations in Two Variables: Equations with two variables, e.g. 2x + 3y = 7.
- Linear Equations in Three Variables: Equations with three variables, e.g. x + 2y + 3z = 10.
Graphing Linear Equations
- The graph of a linear equation is a straight line.
- The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
- The slope (m) represents the change in y over the change in x.
- The y-intercept (b) is the point where the line crosses the y-axis.
Solving Linear Equations
- Addition and Subtraction: Add or subtract the same value to both sides of the equation to isolate the variable.
- Multiplication and Division: Multiply or divide both sides of the equation by the same non-zero value to isolate the variable.
- Graphical Method: Find the point of intersection of two lines on a graph to solve a system of linear equations.
Systems of Linear Equations
- A system of linear equations is a set of two or more linear equations with the same variables.
- Substitution Method: Solve one equation for one variable, then substitute it into the other equation to solve for the other variable.
- Elimination Method: Add or subtract equations to eliminate one variable, then solve for the other variable.
Definition and Notation of Linear Equations
- A linear equation has the highest power of the variable(s) as 1.
- Linear equations can be written in the form ax + by = c, where a, b, and c are constants, and x and y are variables.
Types of Linear Equations
- Simple Linear Equations have only one variable, e.g. 2x = 5.
- Linear Equations in Two Variables have two variables, e.g. 2x + 3y = 7.
- Linear Equations in Three Variables have three variables, e.g.x + 2y + 3z = 10.
Graphing Linear Equations
- The graph of a linear equation is a straight line.
- The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
- The slope (m) represents the change in y over the change in x.
- The y-intercept (b) is the point where the line crosses the y-axis.
Solving Linear Equations
- Addition and Subtraction Method: add or subtract the same value to both sides of the equation to isolate the variable.
- Multiplication and Division Method: multiply or divide both sides of the equation by the same non-zero value to isolate the variable.
- Graphical Method: find the point of intersection of two lines on a graph to solve a system of linear equations.
Systems of Linear Equations
- A system of linear equations is a set of two or more linear equations with the same variables.
- Substitution Method: solve one equation for one variable, then substitute it into the other equation to solve for the other variable.
- Elimination Method: add or subtract equations to eliminate one variable, then solve for the other variable.
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Description
Learn about the definition and types of linear equations, including simple, two-variable, and three-variable equations. Understand the notation and forms of linear equations.
