Systems of Equations (Substitution)

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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 simultaneously.

Front

What is substitution in the context of systems of equations?

Back

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

Front

When is substitution the best method to use?

Back

When one of the equations is already solved for one variable or can be easily manipulated to do so.

Front

Solve the system using substitution: y = 2x + 3, x + y = 10.

Back

(2, 7)

Front

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

Back

Isolate one variable in one of the equations.

Front

Solve the system using substitution: 3x + y = 7, y = 2x - 1.

Back

(2, 3)

Front

What is the graphical interpretation of a solution to a system of equations?

Back

The point where the graphs of the equations intersect.

Front

Solve the system using substitution: y = 4x - 1, 2x + y = 10.

Back

(2, 7)

Front

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

Back

The lines representing the equations are parallel and never intersect.