Solving Systems by Graphing

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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, which represents the solution(s) to the system.

Front

What is the solution to a system of equations?

Back

The values of the variables that satisfy all equations in the system simultaneously.

Front

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

Back

It means that the graphs of the equations are parallel and never intersect.

Front

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

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

How do you graph a linear equation?

Back

You can graph a linear equation by finding two or more points that satisfy the equation and then connecting them with a straight line.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of a line, calculated as the rise (change in y) over the run (change in x).

Front

What is the y-intercept of a line?

Back

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

Front

What is the x-intercept of a line?

Back

The x-intercept is the point where the line crosses the x-axis, represented as (a, 0) in the equation.

Front

How can you determine the solution of a system of equations from a graph?

Back

The solution is found at the point(s) where the graphs of the equations intersect.