Solving Systems using Elimination

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 eliminate a variable in a system of equations?

Back

To remove one variable so that the remaining equation can be solved for the other variable.

Front

What is the elimination method?

Back

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

Front

When using elimination, what do you do if the coefficients of the variables are not the same?

Back

You can multiply one or both equations by a number to make the coefficients the same.

Front

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

Back

Align the equations so that like terms are in the same column.

Front

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

Back

The equations are dependent; they represent the same line and have infinitely many solutions.

Front

What is the solution of a system of equations?

Back

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

Front

How do you check if your solution to a system of equations is correct?

Back

Substitute the values of x and y back into the original equations to see if they hold true.

Front

What happens if the lines represented by the equations are parallel?

Back

The system has no solution because the lines never intersect.

Front

What is the significance of the coefficients in a system of equations?

Back

They determine the slope and position of the lines represented by the equations.