FM 3.5 Solving Systems of Equations by Elimination

Front

What is the elimination method in solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other variable.

Front

What does it mean if two equations have infinite solutions?

Back

Infinite solutions occur when the equations represent the same line, meaning every point on the line is a solution.

Front

What is the first step in the elimination method?

Back

The first step is to manipulate the equations (by multiplying or adding) to align coefficients of one variable for elimination.

Front

What does it mean if two equations have no solution?

Back

No solution occurs when the equations represent parallel lines that never intersect.

Front

How do you determine which equation to multiply in the elimination method?

Back

Choose the equation that will allow you to easily eliminate a variable by matching coefficients with the other equation.

Front

What is the result of multiplying an equation by zero?

Back

Multiplying an equation by zero results in a trivial equation (0=0), which does not provide any useful information.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables that are solved together.

Front

What is the significance of the coefficients in a system of equations?

Back

Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.

Front

What does it mean for two equations to be dependent?

Back

Dependent equations are those that represent the same line, resulting in infinite solutions.

Front

What does it mean for two equations to be independent?

Back

Independent equations are those that represent different lines, resulting in a unique solution or no solution.