Solving Systems 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 a system of equations has no solution?

Back

A system has no solution if the equations represent parallel lines that never intersect.

Front

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

Back

A system has infinitely many solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

How do you create a zero pair in the elimination method?

Back

To create a zero pair, you manipulate one of the equations so that when added to the other equation, one variable cancels out.

Front

What is the first step in solving a system of equations by elimination?

Back

The first step is to align the equations and decide which variable to eliminate.

Front

Given the equations 2x + 3y = 6 and 4x + 6y = 12, what can be said about the system?

Back

The system has infinitely many solutions because the second equation is a multiple of the first.

Front

What is the purpose of multiplying an equation in the elimination method?

Back

Multiplying an equation allows you to create coefficients that can cancel out a variable when the equations are added or subtracted.

Front

Solve by elimination: 3x + 2y = 12 and 6x + 4y = 24. What is the solution?

Back

The system has infinitely many solutions.

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables.

Front

How can you tell if two equations are independent?

Back

Two equations are independent if they represent lines that intersect at exactly one point.