Flashcard E - 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 solve a system using elimination?

Back

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

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines, they will never intersect, indicating no solution.

Front

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

Back

This occurs when the equations represent the same line, meaning every point on the line is a solution.

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

How can you manipulate equations to prepare for elimination?

Back

You can multiply one or both equations by a number to create coefficients that will cancel out one variable.

Front

What is the solution to the system: 2x + 8y = 6 and -5x - 20y = -15?

Back

Many solutions.

Front

What is the solution to the system: 4x + 9y = 28 and -4x - y = -28?

Back

(7,0).

Front

What is the solution to the system: -4x + 9y = 9 and x - 3y = -6?

Back

(9,5).

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.