Task: Solving Systems of Equations by Graphing

Front

What is a system of equations?

Back

A set of two or more linear equations with the same variables.

Front

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

Back

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

Front

What is the solution to a system of equations?

Back

The point where the graphs of the equations intersect, representing the values of the variables that satisfy all equations.

Front

What does it mean if a system of equations has one solution?

Back

There is exactly one point where the two lines intersect, providing a unique solution for the variables.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

How can you determine the solution of a system of equations by graphing?

Back

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

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x) between two points on the line.

Front

What is the y-intercept of a line?

Back

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

Front

What does it mean for two lines to be parallel?

Back

They have the same slope but different y-intercepts, meaning they will never intersect.