6.4 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, allowing you to solve for the other variable.

Front

What is the first step in the elimination method?

Back

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

Front

How do you eliminate a variable in a system of equations?

Back

You can multiply one or both equations by a number to make the coefficients of one variable opposites, then add or subtract the equations.

Front

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

Back

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

Front

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

Back

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

Front

Solve using elimination: 4x + 8y = 20 and -4x + 2y = -30.

Back

(7,-1)

Front

Solve using elimination: 7x + 2y = 24 and 8x + 2y = 30.

Back

(6,-9)

Front

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

Back

(7,0)

Front

What is the solution to the system: 2x + 3y = 6 and 4x + 6y = 12?

Back

Infinite solutions.