Solving Systems by Graphing

Front

What is the solution to a system of equations when two lines intersect?

Back

The solution is the point where the two lines intersect, representing the values of the variables that satisfy both equations.

Front

What does it mean if two lines are parallel in a system of equations?

Back

Parallel lines never intersect, meaning there is no solution to the system of equations.

Front

How can you determine if a system of equations has one solution?

Back

A system has one solution if the lines intersect at exactly one point.

Front

What is the significance of the slope in a system of equations?

Back

The slope indicates the steepness of a line; if two lines have the same slope, they are parallel.

Front

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

Back

It means the two lines are the same line, overlapping completely.

Front

How do you graph a linear equation?

Back

To graph a linear equation, find two or more points that satisfy the equation and connect them with a straight line.

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 y = mx + b.

Front

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

Back

It means the lines are parallel and will never intersect.

Front

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

Back

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