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 the solution of a system of linear equations represent?

Back

The point where the graphs of the equations intersect.

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What is the elimination method?

Back

A method for solving systems of linear equations by removing one variable.

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What is the substitution method?

Back

A method for solving systems of linear equations by substituting one equation into another.

Front

What does 'no solution' mean in the context of linear equations?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the y-intercept in a linear equation?

Back

The point where the line crosses the y-axis.

Front

What is the slope of a line?

Back

The rate at which y changes for a change in x, often represented as 'm' in the equation y = mx + b.

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How do you graph a system of linear equations?

Back

By plotting each equation on the same coordinate plane and finding their intersection.

Front

What is a linear equation?

Back

An equation that makes a straight line when graphed, typically in the form y = mx + b.

Front

What does 'consistent' mean in relation to a system of equations?

Back

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