Systems of Linear Equations (Two Variables)

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

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What does it mean for a solution to a system of linear equations to be an ordered pair?

Back

It means the solution is represented as (x, y), where x and y are the values that satisfy both equations.

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What is the graphical representation of a solution to a system of linear equations?

Back

The point where the lines representing the equations intersect.

Front

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

Back

The lines representing the equations are parallel and never intersect.

Front

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

Back

The lines representing the equations are the same line, meaning every point on the line is a solution.

Front

How do you determine if a point is a solution to a system of linear equations?

Back

Substitute the x and y values of the point into both equations; if both equations are true, the point is a solution.

Front

What is the substitution method for solving systems of linear equations?

Back

Solve one equation for one variable and substitute that expression into the other equation.

Front

What is the elimination method for solving systems of linear equations?

Back

Add or subtract the equations to eliminate one variable, making it easier to solve for the other.

Front

What is the significance of the coefficients in a system of linear equations?

Back

They determine the slope and position of the lines represented by the equations.

Front

What does it mean for two equations to be dependent?

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They represent the same line, resulting in infinite solutions.