6.3 Solving Systems of Equations by Elimination

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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, making it easier to solve for the remaining variable.

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

Back

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

Front

Solve by elimination: 4x + 9y = 28 and -4x - y = -28.

Back

(7, 0)

Front

Solve by elimination: 7x + y = -9 and -3x - y = 5.

Back

(-1, -2)

Front

Solve by elimination: -x + 2y = 17 and 2x + 2y = -10.

Back

(-9, 4)

Front

Solve by elimination: -4x - 2y = -12 and 4x + 8y = -24.

Back

(6, -6)

Front

What is the first step in the elimination method?

Back

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