Systems of Equations- 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 for a system of equations to have a solution?

Back

A solution is a set of values for the variables that makes all equations true, often represented as a point of intersection on a graph.

Front

What is the elimination method in solving systems of equations?

Back

A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is the graphical interpretation of a system of equations?

Back

The solution is the point where the graphs of the equations intersect.

Front

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

Back

It means the lines representing the equations are parallel and never intersect.

Front

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

Back

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

Front

How do you determine the number of solutions in a system of equations?

Back

By analyzing the slopes and intercepts of the lines represented by the equations.

Front

Solve by elimination: 2x + 3y = 6 and 4x - 3y = 12.

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(3, 0)