Solving Systems by Graphing

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

Front

What is the solution to a system of equations?

Back

The point(s) where the equations intersect, representing the values of the variables that satisfy all equations.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations coincide, meaning they are the same line.

Front

How do you graph a linear equation?

Back

Identify the y-intercept and use the slope to find another point, then draw a line through these points.

Front

What is the y-intercept of a linear equation?

Back

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

Front

What is the slope of a line?

Back

The ratio of the rise (change in y) to the run (change in x), often represented as 'm' in the equation y = mx + b.

Front

How can you determine if two lines are parallel?

Back

If they have the same slope but different y-intercepts.

Front

How can you determine if two lines are perpendicular?

Back

If the product of their slopes is -1.