Systems of Equations

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 infinite solutions?

Back

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

Front

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

Back

The equations represent parallel lines that never intersect.

Front

What is the graphical representation of a system of equations?

Back

It can be represented as lines on a coordinate plane.

Front

What is the solution to a system of equations?

Back

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

Front

What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

What does it mean for two lines to be parallel?

Back

They have the same slope but different y-intercepts.

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

How can you determine if two lines are perpendicular?

Back

Their slopes are negative reciprocals of each other.