Solving Systems Using 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 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 the context of solving systems of equations?

Back

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

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 overlap each other, meaning they are the same line.

Front

How can you determine if a system of equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

What is the first step in solving a system of equations using substitution?

Back

Solve one of the equations for one variable in terms of the other.

Front

If you substitute a value into an equation and get a true statement, what does that indicate?

Back

It indicates that the substituted value is a solution to the equation.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation consists of lines or curves on a coordinate plane.

Front

What is the significance of the point of intersection in a system of equations?

Back

It represents the solution to the system, where all equations are satisfied.