Solving Systems of Equations

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

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What does it mean to solve a system of equations?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the graphs of the equations.

Front

What are the possible outcomes when solving a system of equations?

Back

One solution, no solution, or infinitely many solutions.

Front

What does it mean if two lines are parallel in a system of equations?

Back

The system has no solution.

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What does it mean if two lines coincide in a system of equations?

Back

The system has infinitely many solutions.

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What is the substitution method?

Back

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

Front

How do you determine if a system of equations has no solution?

Back

If the equations represent parallel lines.

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How do you determine if a system of equations has infinitely many solutions?

Back

If the equations represent the same line.