Pre-Calculus Chapter 4 Review

Front

What is the elimination method in solving systems of equations?

Back

The elimination method is a technique used to solve systems of equations by adding or subtracting the equations to eliminate one variable, making it easier to solve for the remaining variable.

Front

What is the first step in the elimination method?

Back

The first step is to manipulate the equations (by multiplying, if necessary) so that when added or subtracted, one variable cancels out.

Front

How do you determine which equations to add in the elimination method?

Back

Choose equations that, when added or subtracted, will eliminate one of the variables. This often involves looking for coefficients that are opposites.

Front

What does it mean for two equations to be consistent?

Back

Two equations are consistent if they have at least one solution, meaning their graphs intersect at one or more points.

Front

What does it mean for two equations to be inconsistent?

Back

Two equations are inconsistent if they have no solutions, meaning their graphs are parallel and never intersect.

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 simultaneously.

Front

What is the graphical interpretation of a system of equations?

Back

The graphical interpretation involves plotting the equations on a coordinate plane; the solution(s) are the point(s) where the graphs intersect.

Front

What is the significance of the point of intersection in a system of equations?

Back

The point of intersection represents the solution to the system, indicating the values of the variables that satisfy all equations in the system.

Front

How can you check the solution of a system of equations?

Back

You can check the solution by substituting the values back into the original equations to see if they hold true.

Front

What is a matrix in the context of systems of equations?

Back

A matrix is a rectangular array of numbers that can represent the coefficients of a system of equations, allowing for methods like matrix operations to solve the system.