Systems of Linear Equations (6-1)-(6-3)

Front

What is a system of linear equations?

Back

A collection of two or more linear equations involving the same variables.

Front

What does it mean if a system of linear equations has infinite solutions?

Back

It means that the equations represent the same line, and every point on the line is a solution.

Front

How can you determine if a point is a solution to a system of linear equations?

Back

By substituting the x and y values of the point into each equation and checking if both equations are satisfied.

Front

What does it mean if a system of linear equations has no solutions?

Back

It means that the lines represented by the equations are parallel and never intersect.

Front

What is the graphical representation of a system with one solution?

Back

Two lines that intersect at a single point.

Front

What are parallel lines in the context of linear equations?

Back

Lines that have the same slope but different y-intercepts, indicating they will never meet.

Front

What is the significance of the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it travels (positive or negative).

Front

What is the y-intercept in a linear equation?

Back

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

Front

How can you find the solution to a system of equations graphically?

Back

By plotting the equations on a graph and identifying the point(s) where the lines intersect.

Front

What does it mean for two lines to be coincident?

Back

It means that the two lines lie on top of each other, representing infinite solutions.