Linear Systems Alg/Gr

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 if a linear system has one solution?

Back

It means the lines represented by the equations intersect at exactly one point.

Front

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

Back

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

Front

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

Back

It means the lines represented by the equations are the same line, overlapping each other.

Front

How can you determine the number of solutions in a linear system?

Back

By analyzing the slopes and y-intercepts of the lines represented by the equations.

Front

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

Back

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

Front

How do you solve a system of equations by graphing?

Back

You graph both equations on the same coordinate plane and identify the point(s) where they intersect.

Front

What is the significance of the point of intersection in a linear system?

Back

The point of intersection represents the solution to the system, giving the values of the variables that satisfy both equations.

Front

What is the graphical representation of a system with no solutions?

Back

Two parallel lines that never intersect.

Front

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

Back

Two lines that intersect at a single point.