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 the substitution method?

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A method for solving a system 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?

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

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What is an isolated variable?

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A variable that is expressed alone on one side of an equation.

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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 solving a system of equations by substitution?

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Solve one of the equations for one variable.