Systems of Linear Equations

Front

What are the three main methods used to solve a system of linear equations?

Back

Graphing, Elimination, Substitution.

Front

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

Back

The graphs of the equations intersect at exactly one point.

Front

What is the elimination method in solving systems of linear equations?

Back

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

Front

What is the substitution method in solving systems of linear equations?

Back

A method that involves solving one equation for a variable and substituting that expression into the other equation.

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 graphs of the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you graph a linear equation?

Back

Find two or more points that satisfy the equation and connect them with a straight line.

Front

What is the purpose of finding the slope in a linear equation?

Back

The slope indicates the steepness of the line and the direction it goes (rise over run).

Front

What is an additive inverse in the context of the elimination method?

Back

An additive inverse is a number that, when added to another number, results in zero, used to eliminate a variable.