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 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 a zero pair in the context of elimination?

Back

A zero pair occurs when two terms cancel each other out, resulting in a sum of zero.

Front

How do you create a zero pair in a system of equations?

Back

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

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

What is the solution to the system: -6x + 6y = 0 and 9x - 8y = 4?

Back

(4, 4)

Front

What is the solution to the system: 3x + 2y = 16 and 7x + y = 19?

Back

(2, 5)

Front

What is the solution to the system: 7x + y = -9 and -3x - y = 5?

Back

(-1, -2)

Front

How do you check the solution of a system of equations?

Back

Substitute the solution back into the original equations to see if both equations are satisfied.

Front

What is the significance of having no solution in a system of equations?

Back

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