Algebra Systems Review

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the set of all points that satisfy all inequalities in the system.

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How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution to a system of equations if it satisfies all equations in the system when the coordinates of the point are substituted into the equations.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the appropriate region that satisfies the inequality.

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What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value). A relation can have multiple outputs for a single input.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

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How do you find the intersection of two lines represented by equations?

Back

To find the intersection, solve the system of equations simultaneously to find the point (x, y) where the two lines meet.

Front

What is a setup fee in a cost equation?

Back

A setup fee is a fixed charge that must be paid before any additional costs are incurred, often represented as a constant in a cost equation.

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What does it mean for a system of equations to be consistent?

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A system of equations is consistent if there is at least one solution. It can be either independent (one solution) or dependent (infinitely many solutions).