Solving 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 to solve a system of linear equations?

Back

Finding the values of the variables that satisfy all equations in the system.

Front

What is the substitution method?

Back

A method for solving systems of equations by solving one equation for one variable and substituting that expression into the other equation.

Front

What is the elimination method?

Back

A method for solving systems of equations by adding or subtracting equations to eliminate one variable.

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What does it mean if a system has no solution?

Back

The lines represented by the equations are parallel and never intersect.

Front

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

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The equations represent the same line, meaning every point on the line is a solution.

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What is a unique solution in a system of equations?

Back

A single point where the lines intersect, representing one set of values for the variables.

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How do you determine if a system of equations is consistent?

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

Front

How do you determine if a system of equations is inconsistent?

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A system is inconsistent if it has no solutions.

Front

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

Back

The lines of the equations plotted on a coordinate plane.