Solving Systems of Equations

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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.

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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 substitution 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 elimination 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 check the solution of a system of equations?

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Substitute the solution back into the original equations to verify if both equations are satisfied.

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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 identifying 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 the first step in using substitution to solve a system of equations?

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Solve one of the equations for one variable in terms of the other.

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What is the first step in using elimination to solve a system of equations?

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Align the equations so that corresponding variables and constants are in the same columns.