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?

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

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What is the substitution method in solving systems of equations?

Back

A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving systems of equations?

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A method where equations are added or subtracted to eliminate one variable, making it easier to solve for the other.

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What is a consistent system of equations?

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A system that has at least one solution.

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What is an inconsistent system of equations?

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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.

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How do you graph a system of equations?

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By plotting each equation on the same coordinate plane and identifying the point(s) where they intersect.

Front

What does the intersection point of two lines represent in a system of equations?

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The solution to the system, which is the set of values for the variables that satisfy both equations.

Front

What is the first step in the substitution method?

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Substitute in the value of the isolated variable into the other equation.