Systems of Equations by 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 you to solve for the other 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 infinite solutions?

Back

It means the equations represent the same line, so there are countless points of intersection.

Front

Solve using Elimination Method: 4x + 9y = 28 and -4x - y = -28.

Back

(7,0)

Front

Solve using Elimination Method: 4x + y = 6 and x - 2y = 6.

Back

(2,-2)

Front

Solve using Elimination Method: 9x - 4y = 7 and x - 4y = -17.

Back

(3,5)

Front

Solve using Elimination Method: x - y = 11 and 2x + y = 19.

Back

(10,-1)

Front

What is the first step in the elimination method?

Back

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