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 infinite solutions?

Back

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

Front

What is the substitution method in solving systems of equations?

Back

A method where one variable is isolated in one equation and substituted into another equation.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable.

Front

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

Back

The equations represent two intersecting lines, and the point of intersection is the solution.

Front

What is the graphical representation of a system of equations with no solution?

Back

The equations represent parallel lines that never intersect.

Front

What is the first step in the substitution method?

Back

Isolate one variable in one of the equations.

Front

What is the first step in the elimination method?

Back

Align the equations and manipulate them to create opposite coefficients.

Front

What is the purpose of finding the slope in a system of equations?

Back

To determine the steepness of the lines and their relationship (parallel, intersecting, or coincident).

Front

What is an additive inverse?

Back

A number that, when added to another number, results in zero.