Systems 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 removing one variable, making it easier to solve for the other.

Front

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

Back

It indicates that the lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has an infinite number of solutions?

Back

It means that the equations represent the same line, and every point on that line is a solution.

Front

How do you determine if two equations are equivalent?

Back

Two equations are equivalent if they have the same solution set.

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

If you have the equations 4x + 4y = 4 and 3x + 4y = 10, what is the next step after aligning them?

Back

Subtract the second equation from the first to eliminate y.

Front

What is the solution to the system of equations 3x + 7y = 23 and -3x - 7y = -17?

Back

No solution, as the equations represent parallel lines.

Front

What does it mean if the coefficients of x and y are the same in two equations?

Back

It may indicate that the equations are dependent, leading to either no solution or infinite solutions.