Solving Systems by Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that can be 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, making it easier to solve for the remaining variable.

Front

How do you set up a system of equations from a word problem?

Back

Identify the variables, translate the relationships into equations, and write them in standard form.

Front

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

Back

Align the equations so that corresponding variables and constants are in the same columns.

Front

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

Back

The two equations represent the same line, so there are infinitely many solutions.

Front

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

Back

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

Front

What does it mean if a system of equations has exactly one solution?

Back

It means the lines intersect at a single point, representing the values of the variables.

Front

How can you check your solution after solving a system of equations?

Back

Substitute the values back into the original equations to see if they hold true.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

Front

What is a coefficient in an equation?

Back

A numerical factor that multiplies a variable in an equation.