Solving Systems of Equations

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 are the three main methods for solving systems of equations?

Back

Substitution, Elimination, and Graphing.

Front

When is substitution the best method to use?

Back

When one equation is already solved for one variable.

Front

When is elimination the best method to use?

Back

When both equations are in standard form and can be easily manipulated to eliminate a variable.

Front

What is the substitution method?

Back

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

Front

What is the elimination method?

Back

A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

Front

How do you graph a system of equations?

Back

By plotting each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

What does it mean if two lines intersect at one point?

Back

The system has one unique solution.

Front

What does it mean if two lines are parallel?

Back

The system has no solution, as the lines never intersect.