Systems of Equations

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?

Back

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

Front

What is the graphical representation of a system of equations?

Back

The intersection points of the lines representing the equations on a graph.

Front

What is a consistent system of equations?

Back

A system that has at least one solution.

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What is an inconsistent system of equations?

Back

A system that has no solutions.

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What is a dependent system of equations?

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A system that has infinitely many solutions, where the equations represent the same line.

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.

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What is the elimination method?

Back

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

Front

How do you check the solution of a system of equations?

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By substituting the solution back into the original equations to see if they hold true.

Front

What is the solution to the system: x = 7 - 2y and 2x + y = 5?

Back

(1, 3)