System 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 elimination method?

Back

A technique for solving systems of equations by removing one variable, allowing for easier solving.

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What does it mean if a system of equations has no solution?

Back

The equations represent parallel lines that never intersect.

Front

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

Back

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

Front

How can you identify a system of equations with no solution graphically?

Back

The graph will show parallel lines.

Front

How can you identify a system of equations with infinitely many solutions graphically?

Back

The graph will show the same line drawn multiple times.

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What is the substitution method?

Back

A technique 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 graphical method of solving a system of equations?

Back

Plotting both equations on a graph and identifying the point(s) of intersection.

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What is a consistent system of equations?

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A system that has at least one solution.