Solutions to linear system from graphs

Front

What is a linear system of equations?

Back

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

Front

What does it mean for a linear system to have a unique solution?

Back

A linear system has a unique solution when the graphs of the equations intersect at exactly one point.

Front

What does it mean for a linear system to have no solution?

Back

A linear system has no solution when the graphs of the equations are parallel and never intersect.

Front

What does it mean for a linear system to have infinitely many solutions?

Back

A linear system has infinitely many solutions when the equations represent the same line, meaning they overlap completely.

Front

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

Back

You can determine the solution by graphing the equations and identifying the point(s) where the lines intersect.

Front

What is the graphical representation of the solution (3, 2)?

Back

The point (3, 2) is the intersection of the lines represented by the equations in the system.

Front

What is the significance of the point (-2, -1) in a linear system?

Back

The point (-2, -1) is the unique solution to the system, indicating where the two lines intersect.

Front

What does it indicate if two lines in a linear system are parallel?

Back

If two lines are parallel, it indicates that the system has no solution.

Front

What is the first step in solving a system of equations graphically?

Back

The first step is to graph each equation on the same coordinate plane.

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.