Systems of Linear Equations

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 when a system of linear equations has no solution?

Back

The lines representing the equations are parallel and never intersect.

Front

What does it mean when a system of linear equations has one solution?

Back

The lines representing the equations intersect at exactly one point.

Front

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

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The lines representing the equations coincide, meaning they are the same line.

Front

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

Back

Graphing each equation on the same coordinate plane and identifying the point of intersection.

Front

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

Back

Isolating one variable in one equation and substituting it into the other equation.

Front

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

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Adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

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

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

Front

How can you determine if a system of equations is consistent or inconsistent?

Back

A consistent system has at least one solution, while an inconsistent system has no solutions.

Front

What is an additive inverse in the context of elimination?

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An additive inverse is a number that, when added to another number, results in zero, used to eliminate variables.