Systems of Linear Equations and Inequalities Review

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What is a system of linear equations?

Back

A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect.

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What does it mean for a system of equations to be consistent?

Back

A system of equations is consistent if it has at least one solution.

Front

What does it mean for a system of equations to be inconsistent?

Back

A system of equations is inconsistent if it has no solutions.

Front

What does it mean for a system of equations to be dependent?

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A system of equations is dependent if it has infinitely many solutions, meaning the equations represent the same line.

Front

What is the substitution method for solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

What is the elimination method for solving systems of equations?

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

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How do you classify a system of equations with exactly one solution?

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A system with exactly one solution is classified as consistent and independent.

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

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The graphical representation of a system of linear equations is the intersection point(s) of the lines representing the equations.

Front

What is the significance of the slope in a linear equation?

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The slope indicates the steepness of the line and the direction of the relationship between the variables.

Front

How can you determine if two lines are parallel?

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Two lines are parallel if they have the same slope but different y-intercepts.