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 to solve a system of equations by graphing?

Back

It means to find the point(s) where the graphs of the equations intersect.

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 two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis.

Front

What does it mean if two lines are parallel?

Back

Parallel lines have the same slope and will never intersect.

Front

What does it mean if two lines are perpendicular?

Back

Perpendicular lines intersect at a right angle and their slopes are negative reciprocals.

Front

What is the solution to a system of equations if the lines intersect at one point?

Back

There is one unique solution, which is the coordinates of the intersection point.

Front

What does it mean if two lines coincide?

Back

If two lines coincide, they lie on top of each other and have infinitely many solutions.

Front

What is the graphical representation of no solution in a system of equations?

Back

The lines are parallel and do not intersect.