Solving Systems of Equations Using Elimination by Multiplication

Front

What is a system of equations?

Back

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

Front

What does it mean to solve a system of equations?

Back

Finding the values of the variables that satisfy all equations in the system simultaneously.

Front

What is the elimination method in solving systems of equations?

Back

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

Front

How do you use multiplication in the elimination method?

Back

You multiply one or both equations by a number to align coefficients, allowing for the elimination of a variable.

Front

What is the first step in using the elimination method?

Back

Arrange the equations in standard form (Ax + By = C) if they are not already.

Front

Given the equations 2x + 3y = 6 and 4x + 6y = 12, what can you conclude?

Back

The system has an infinite number of solutions because the second equation is a multiple of the first.

Front

What is a unique solution in a system of equations?

Back

A unique solution occurs when the lines represented by the equations intersect at exactly one point.

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What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

Solve the system using elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinite number of solutions.

Front

Solve the system using elimination: 3x + 2y = 12 and 6x + 4y = 24.

Back

Infinite number of solutions.