Solving Systems by Elimination (Multiply First)

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 by elimination?

Back

It means to eliminate one variable by adding or subtracting the equations, allowing the other variable to be solved.

Front

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

Back

Multiply one or both equations by a number to align coefficients for one variable.

Front

Given the equations 4x - 6y = -6 and -2x - 12y = -12, what is the first step to eliminate x?

Back

Multiply the first equation by 1 and the second equation by 2 to align the coefficients of x.

Front

What is the solution to the system 4x - 6y = -6 and -2x - 12y = -12?

Back

(0, 1)

Front

What is the purpose of multiplying an equation in a system before elimination?

Back

To create equivalent equations that make it easier to eliminate a variable.

Front

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

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Front

What is the elimination method?

Back

A method for solving systems of equations by removing one variable, allowing for the other to be solved.

Front

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

Back

The lines represented by the equations are parallel and do not intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.