Systems of Linear Equations

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean if a system of linear equations has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system of linear equations has infinitely many solutions?

Back

The lines coincide, meaning they are the same line.

Front

What are the three main methods to solve systems of equations?

Back

Graphing, Substitution, Elimination.

Front

How do you determine if a point is a solution to a system of equations?

Back

Substitute the point into both equations; if it satisfies both, it is a solution.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate a variable.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for a variable and substituting that expression into the other equation.

Front

Solve the system: 2x + 3y = 6 and x - y = 1. What is the solution?

Back

(3, 0) is the solution.

Front

What is the graphical representation of a system of linear equations?

Back

The lines representing the equations on a coordinate plane.