Solving Systems of Equations 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 two lines are parallel when graphing a system of equations?

Back

It means there is no solution to the system, as the lines never intersect.

Front

What does it mean if two lines coincide when graphing a system of equations?

Back

It means there are infinitely many solutions, as the lines overlap completely.

Front

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

Back

By identifying the coordinates of the intersection point of the lines on the graph.

Front

What is the significance of the coordinates (x, y) in a solution?

Back

They represent the values of the variables that satisfy both equations in the system.

Front

What is the first step in graphing a system of equations?

Back

Rewrite each equation in slope-intercept form (y = mx + b) if necessary.

Front

What does the term 'slope' refer to in the context of a linear equation?

Back

The slope (m) indicates the steepness of the line and the direction it goes (rise over run).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis (when x = 0).