System 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 to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is substitution 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 elimination 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 if a system of equations has no solution?

Back

The lines represented by the equations are parallel and never intersect.

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 is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations on a graph.

Front

What is the solution to the system y = 4x + 3 and 2x - 3y = 21?

Back

(-3, -9)

Front

What is the solution to the system -4x - 4y = 0 and 4x + 4y = 0?

Back

Infinite number of solutions.

Front

What does it mean for intersecting lines in a system of equations?

Back

They have exactly one solution, which is the point of intersection.