Algebra

Systems of Linear Inequalities

One way to solve systems of linear equalities is to graph the inequalities and see if there are any areas on the graph where the inequalities overlap. The places where the inequalities’ graphs overlap are the solutions to the system.

Linear Systems: Solve by Elimination

Systems of linear equations with two or more variables (and equations) can be solved in various ways, including adding, subtracting, and multiplying the equations together in order to eliminate a variable. These methods are often faster than graphing the equations or using the substitution method.

Linear Systems: Solve by Graphing & Substitution

To find the solutions for systems of linear equations, the graphing method or substitution may be employed. However, not every system has exactly one solution. Some systems may have more than one solution and some may have no solutions at all.

Determining The Equation of a Line

The equation of the line can reveal a lot about the function it represents. The slope of the equation represents how fast and in what direction the function is moving. The intercept of the equation reveals how the function relates to the axes. The equation of a particular line can also help predict future values for that function.

Graphing Linear Equations

Graphs and functions are critical, not only for solving math problems, but for real life situations. They can be used, for example, to find trends in data. None of this is possible, however, without first knowing the basic foundation of graphing, the different forms that an equation can be written in, or how to write these equations. These basics will be used for all types of more complex graphing in the future.

Lines in the Coordinate Plane

In addition to having many properties involving transversals, parallel and perpendicular lines also have special relationships on the coordinate plane involving slope. Two parallel lines always have the same slope, and perpendicular lines have slopes that are negative reciprocals of each other. Equations can be written in slope-intercept form to make it easier for us to graph them and find their slopes.

Absolute Value: Equations & Inequalities

Absolute value equations and inequalities are very similar to linear equations and inequalities. In both cases, the goal is to solve for a variable. However, unlike linear equations and linear inequalities, the variable is not a specific number. Instead, the variable represents a specific distance from zero. When solving absolute value equations and inequalities, two options need to be considered: when the expression inside the absolute value is not negative and when the expression inside the absolute value is negative.

Compound Inequalities

Compound inequalities refer to a group of multiple inequalities joined by either “and” or “or”. Venn diagrams are a good visual way to represent the solutions to the compound inequalities. Each circle in a Venn diagram represents the set of solutions for each individual inequality.

Linear equations

A mathematical expression is like a “phrase” that includes numbers, operations, and variables, while a mathematical equation is like a “sentence” where two expressions are set equal to each other. Solving linear equations with one variable involves using properties of equality and the order of operations to solve for that unknown variable.

Number Lines

Real numbers can be visualized using a number line. Number lines are helpful for picturing a number of algebra concepts, including opposite numbers, operations of real numbers, and inequalities.

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