Solving Systems with 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?

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 eliminating one variable, allowing for the other to be solved.

Front

What is a solution to a system of equations?

Back

A set of values for the variables that makes all equations true.

Front

What does it mean if a system has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

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

Back

The equations represent the same line, meaning every point on the line is a solution.

Front

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

Back

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

Front

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

Back

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

Front

Solve by elimination: 7x - y = 10 and -7x + y = -14.

Back

No Solution.

Front

Solve by elimination: -6x + 5y = 1 and 6x + 4y = -10.

Back

(-1, -1).