Solving Systems of Equations by Graphing

Front

What is the solution to the system of equations represented by the intersection of two lines?

Back

The solution is the point where the two lines intersect, which represents the values of x and y that satisfy both equations.

Front

How can you tell if a point (x, y) is a solution to a system of equations?

Back

The (x, y) coordinates satisfy both equations.

Front

If a system of equations has infinitely many solutions, what does that imply about the lines?

Back

The lines will overlap each other.

Front

Why do parallel lines never intersect?

Back

They have the same slope.

Front

What happens when you graph the same equation twice?

Back

You will have infinitely many solutions.

Front

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

Back

It means the system of equations has one unique solution.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the lines of the equations on a coordinate plane.

Front

What does it indicate if two lines are parallel?

Back

It indicates that the system of equations has no solution.

Front

What is the slope of a line?

Back

The slope is a measure of the steepness of the line, calculated as the rise over run.

Front

How do you find the slope of a line given two points?

Back

Use the formula: slope (m) = (y2 - y1) / (x2 - x1).