Linear Systems Review

Front

What is a linear system?

Back

A linear system is a collection of one or more linear equations involving the same variables.

Front

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

Back

A point is a solution to a linear system if it satisfies all equations in the system.

Front

What is the graphical representation of a linear equation?

Back

A linear equation is represented graphically as a straight line.

Front

What is the intersection of two lines in a linear system?

Back

The intersection is the point where the two lines meet, representing the solution to the system.

Front

Define the term 'slope' in the context of linear equations.

Back

The slope is a measure of the steepness of a line, calculated as the rise over run.

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.

Front

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

Back

Substitute the point into each inequality; if it satisfies all, it is a solution.

Front

What is the standard form of a linear equation?

Back

The standard form is Ax + By = C, where A, B, and C are integers.

Front

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

Back

A consistent system has at least one solution.

Front

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

Back

An inconsistent system has no solutions.