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 for two lines to intersect?

Back

It means they have a common solution, which is the point where they meet.

Front

What is the solution to a system of equations?

Back

The point (x, y) that satisfies all equations in the system.

Front

How can you determine if a system of equations has no solution?

Back

If the lines are parallel, they will never intersect.

Front

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

Back

The equations represent the same line, so every point on the line is a solution.

Front

What is the graphical method for solving systems of equations?

Back

Plotting the equations on a graph and identifying the intersection point.

Front

What is the slope of a line?

Back

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

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis (x=0).

Front

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

Back

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

Front

What is the significance of the point (1, -4) in a system of equations?

Back

It is the solution to the system, meaning it satisfies both equations.