System of Equations 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 of equations 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 elimination method?

Back

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

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

If the lines intersect at one point, there is one solution; if they are parallel, there is no solution; if they are the same line, there are infinitely many solutions.

Front

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

Back

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

Front

Given the equations 2x + 3y = 6 and 4x + 6y = 12, what can be said about the system?

Back

The system has infinitely many solutions because the second equation is a multiple of the first.

Front

Solve the system: 2x + y = 10 and x - y = 2.

Back

(4, 2) - This is the solution to the system.

Front

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

Back

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

Front

How can you check your solution to a system of equations?

Back

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

Front

What does it mean if two equations in a system are dependent?

Back

It means they represent the same line and have infinitely many solutions.