Solving Systems of Equations

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 are the three main methods for solving systems of equations?

Back

Graphing, substitution, and elimination.

Front

When is the substitution method most useful?

Back

When one equation is easily solvable for one variable.

Front

What is the elimination method?

Back

A technique that involves adding or subtracting equations to eliminate a variable.

Front

How do you check if a solution is correct for a system of equations?

Back

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

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

Solve by elimination: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)

Front

Which method is best for the system: y = 6x - 11 and -2x - 3y = -7?

Back

Substitution because a variable is isolated.