Solving Systems Graphically Flashcard

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 two equations have a common solution, represented by the point of intersection.

Front

What is the graphical representation of a linear equation?

Back

A straight line on a coordinate plane.

Front

What does it mean if two lines are parallel on a graph?

Back

They have the same slope and will never intersect, indicating no solution to the system.

Front

What is the slope of a line?

Back

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

Front

How do you find the slope from an equation in standard form?

Back

Convert the equation to slope-intercept form (y = mx + b) to identify the slope (m).

Front

What is the slope-intercept form of a linear equation?

Back

y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

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

Front

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

Back

If the lines are parallel and do not intersect, the system has no solution.

Front

What is the y-intercept of a line?

Back

The point where the line crosses the y-axis, represented as (0, b) in the equation y = mx + b.