Solving systems of equations review

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What is a system of equations?

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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?

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

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What is the substitution method in solving systems of equations?

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

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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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How do you solve the equation x + 3y = 9 for x?

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x = 9 - 3y.

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What is the graphical method of solving systems of equations?

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Plotting the equations on a graph and finding the point(s) where they intersect.

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

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The system has no solution because the lines never intersect.

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

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The system has infinitely many solutions because the lines are the same.

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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.