Systems of Equations

Front

What are systems of equations?

Back

A set of two or more equations with the same variables that are solved together.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Front

What is the solution of a system of equations?

Back

The point(s) where the equations intersect on a graph.

Front

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

Back

The lines representing the equations are parallel and do not intersect.

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 one solution?

Back

If the lines intersect at exactly one point, the system has one solution.

Front

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

Back

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

Front

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

Back

The slope (m) is calculated as (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 (x=0).

Front

What is the graphical representation of a system of equations?

Back

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