5-2: Solve 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 graph the equations on the same coordinate plane and find the point(s) where they intersect.

Front

What is the solution to a system of equations?

Back

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

Front

What does it mean if two lines intersect at one point?

Back

The system has one unique solution.

Front

What does it mean if two lines are parallel?

Back

The system has no solution because the lines never intersect.

Front

What does it mean if two lines are the same?

Back

The system has infinitely many solutions because every point on the line is a solution.

Front

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

Back

By analyzing the slopes and y-intercepts of the lines: if slopes are different, one solution; if slopes are the same and y-intercepts are different, no solution; if both are the same, infinitely many solutions.

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x (rise/run).

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 is the standard form of a linear equation?

Back

Ax + By = C, where A, B, and C are integers and A is non-negative.