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 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.

Front

What is the graphical method for solving systems of equations?

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Plotting each equation on a graph and identifying the point(s) where they intersect.

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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.

Front

What is the elimination method in solving systems of equations?

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A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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

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The lines representing the equations are parallel and never intersect.

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

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

Front

How do you determine the solution of a system of equations graphically?

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The solution is the point(s) where the graphs of the equations intersect.

Front

What is the first step in using the substitution method?

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

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What is the purpose of the elimination method?

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To simplify the system of equations by eliminating one variable to solve for the other.