Solving Systems By Elimination

Front

What is a coefficient in an algebraic expression?

Back

A coefficient is a number that is multiplied by a variable in an algebraic expression.

Front

How do you solve a system of equations by elimination?

Back

To solve by elimination, you manipulate the equations to eliminate one variable, allowing you to solve for the other variable.

Front

What is the purpose of creating a zero pair in elimination?

Back

Creating a zero pair allows you to eliminate one variable from the equations, simplifying the system to a single equation.

Front

What does it mean to multiply an equation to create a zero pair?

Back

It means to multiply one or both equations by a number so that when added or subtracted, one variable cancels out.

Front

What is the solution to a system of equations?

Back

The solution is the point (x, y) where the two equations intersect, representing the values of the variables that satisfy both equations.

Front

What is the first step in solving the system 4x + 9y = 28 and -4x - y = -28 by elimination?

Back

The first step is to add the two equations together to eliminate the variable x.

Front

What is the significance of the term 'elimination' in solving systems of equations?

Back

Elimination refers to the process of removing one variable to solve for the other, making it easier to find the solution.

Front

How can you determine which variable to eliminate in a system of equations?

Back

You can choose to eliminate the variable that has coefficients that are easier to manipulate or that will create simpler calculations.

Front

What is the result of the elimination method if the two equations are dependent?

Back

If the equations are dependent, they represent the same line, and there are infinitely many solutions.

Front

What is the result of the elimination method if the two equations are inconsistent?

Back

If the equations are inconsistent, they represent parallel lines, and there is no solution.