8R U4:Systems: Substitution & Elimination Methods

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?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the elimination method?

Back

A technique for solving systems of equations by removing one variable, making it easier to solve for the other.

Front

What does it mean if a system has infinitely many solutions?

Back

The equations represent the same line, so there are countless points that satisfy both equations.

Front

What is a unique solution in a system of equations?

Back

A single pair of values for the variables that satisfies all equations in the system.

Front

What does it mean if a system has no solution?

Back

The equations represent parallel lines that never intersect.

Front

How do you eliminate a variable in the elimination method?

Back

You can add or subtract the equations to cancel out one of the variables.

Front

What is the first step in solving a system of equations by elimination?

Back

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

Front

Solve the system: 2x + 3y = 6 and 4x + 6y = 12.

Back

Infinitely many solutions.

Front

Solve the system: x + y = 5 and x - y = 1.

Back

(3, 2).