Solving Systems by Substitution and Elimination

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 is the first step in the substitution method?

Back

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

Front

What is the first step in the elimination method?

Back

Align the equations and manipulate them to eliminate one variable.

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 infinitely many solutions?

Back

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

Front

How do you check your solution for a system of equations?

Back

Substitute the values back into the original equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The points where the lines intersect represent the solutions to the system.