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?

Back

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

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What is a solution to a system of equations?

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A set of values for the variables that makes all equations true.

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What are the possible types of solutions for a system of equations?

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One solution, no solution, or infinitely many solutions.

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

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The equations represent parallel lines that 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 can you determine if a system of equations has one solution?

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If the lines represented by the equations intersect at exactly one point.

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What is the substitution method for solving systems of equations?

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Solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method for solving systems of equations?

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Adding or subtracting equations to eliminate one variable, making it easier to solve.

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What is the graphical method for solving systems of equations?

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Plotting the equations on a graph and identifying the point(s) of intersection.