Solving 3-variable systems REVIEW

Front

What is a system of equations?

Back

A set of two or more equations with the same variables that are solved together.

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What does it mean to solve a system of equations by elimination?

Back

Elimination involves adding or subtracting equations to eliminate one variable, making it easier to solve for the others.

Front

What does it mean to solve a system of equations by substitution?

Back

Substitution involves solving one equation for one variable and then substituting that expression into another equation.

Front

What is the solution to a system of equations?

Back

The solution is the set of values for the variables that makes all equations in the system true.

Front

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

Back

It means that the equations represent the same line or plane, and there are countless points that satisfy all equations.

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What is a consistent system of equations?

Back

A consistent system has at least one solution.

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What is an inconsistent system of equations?

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An inconsistent system has no solutions, meaning the equations represent parallel lines that never intersect.

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How can you check if your solution to a system of equations is correct?

Back

You can substitute the solution back into the original equations to see if they hold true.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation shows the lines or planes of the equations, where the intersection points represent the solutions.

Front

What is the first step in solving a system of equations by elimination?

Back

Identify which variable to eliminate and manipulate the equations accordingly.