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 for the other variable to be solved.

Front

What is the elimination method?

Back

A method for solving systems of equations by combining equations to eliminate one variable.

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 is an infinite number of solutions in a system of equations?

Back

When the equations represent the same line, every point on the line is a solution.

Front

Solve by elimination: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinite solutions (the second equation is a multiple of the first).

Front

Solve by elimination: 5x - 2y = 3 and 10x - 4y = 6.

Back

Infinite solutions (the second equation is a multiple of the first).

Front

Solve by elimination: 3x + 4y = 10 and 3x + 4y = 14.

Back

No solution (the lines are parallel).

Front

What is the first step in the elimination method?

Back

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

Front

How can you make the coefficients of one variable the same in both equations?

Back

Multiply one or both equations by a number to achieve the same coefficient for one variable.