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 for two lines to intersect on a graph?

Back

It means that the solution to the system of equations is the point where the two lines meet.

Front

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

Back

By plotting both equations on the same graph and identifying the point of intersection.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis.

Front

How do you determine the slope of a line from its graph?

Back

The slope is the rise over run, calculated as the change in y divided by the change in x.

Front

What does it mean if two lines are parallel?

Back

They have the same slope and will never intersect, meaning there is no solution to the system.

Front

What is the significance of the solution to a system of equations?

Back

It represents the values of the variables that satisfy all equations in the system.

Front

What is an example of a system of equations with no solution?

Back

y = 2x + 1 and y = 2x - 3 are parallel lines.

Front

What is an example of a system of equations with infinitely many solutions?

Back

y = 2x + 1 and 2y = 4x + 2 are the same line.

Front

How do you find the x-intercept of a line?

Back

Set y = 0 in the equation and solve for x.