Systems of Equations: Substitution

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

It means that the equations represent the same line, and every point on that line is a solution.

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, resulting in no solution.

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 first step in using the substitution method?

Back

Isolate one variable in one of the equations.

Front

What does the solution (6, 3) represent in a system of equations?

Back

It represents the point where the two equations intersect on a graph.

Front

What is the significance of the point (11, 21) in a system of equations?

Back

It is the unique solution where both equations are satisfied.

Front

How can you graphically represent a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying their intersection points.

Front

What does it mean if two equations in a system are identical?

Back

They represent the same line, leading to infinite solutions.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.