Chapter 3
Algebraic Linear Equations
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Key Concepts
1. A linear equation can have one or more variables
2. Solving a linear equation involves applying arithmetic and algebraic rules
3. A linear equation may have one solution, no solution, or infinitely many solutions
4. A consistent equation in one variable is an equation that has one solution
5. An inconsistent equation is an equation that has no solution
6. An identity is an equation that is true for all values of the variable
7. A linear relationship between two variables can be represented with an equation or a table
of values
8. Solving for a variable in a multi-variable linear equation means expressing the variable in
terms of the other variables
9. Linear equations can be used to represent and solve real-world problems
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Map
Chapter 4
Lines and Linear Equations
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Key Concepts
1. The slope-intercept form of a linear equation is given by 𝑦 = 𝑚𝑥 + 𝑏, where 𝑚
represents the slope and 𝑏 is the 𝑦-intercept of the graph of the equation
2. The slope of a line passing through two points (𝑥 , 𝑦 ) and (𝑥 , 𝑦 ) is equal to
or
3. The slope is always the same between any two distinct points on a line and can be
positive, negative, zero, or undefined
4. The 𝑦-intercept, 𝑏, is the 𝑦-coordinate of the point where a line intersects the 𝑦-axis
5. The equation of a horizontal line through the point (𝑐, 𝑑) is 𝑦 = 𝑑. The equation of a
vertical line through the point (𝑐, 𝑑) is 𝑥 = 𝑐
6. You can write an equation of a line given the slope 𝑚 and the 𝑦-intercept 𝑏, the slope 𝑚
and a point, or the coordinates of two points
7. You can write an equation of a line parallel to a given line if you know the 𝑦-intercept of
the line you want to draw, or the coordinates of a point on the line you want to draw
8. You can use linear equations and graphs to model and solve real-world problems
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Map
Chapter 5
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Key Concepts
A set of linear equations with more than one variable is called a system of linear equations
A system of linear equation can have a unique solution, no solution, or infinitely many
solutions
A system of linear equations can be solved algebraically by using:
The Elimination Method
Eliminate one variable by adding or subtracting two equations with a common
term
The Substitution Method
Solve one equation for one variable and substitute the expression into the other
equation
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Maps