System of Equations Graphs

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, meaning they overlap completely.

Front

What is the solution to a system of equations?

Back

The point(s) where the graphs of the equations intersect.

Front

How can you determine the solution of a system of equations graphically?

Back

By finding the point(s) where the lines intersect on the graph.

Front

What is the graphical representation of the equation y = 2x + 1?

Back

A straight line with a slope of 2 and a y-intercept of 1.

Front

What is the slope of a line?

Back

The rate at which the line rises or falls, calculated as the change in y over the change in x.

Front

What does it mean for two lines to be perpendicular?

Back

They intersect at a right angle (90 degrees) and have slopes that are negative reciprocals of each other.

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.

Front

How do you find the solution to a system of equations algebraically?

Back

By using methods such as substitution, elimination, or graphing.