Solving Systems of Equations - Substitution

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What is a system of equations?

Back

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 the substitution method in solving systems of equations?

Back

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

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

Back

The lines represented by the equations are parallel and never intersect.

Front

What does it mean if a system of equations has infinite 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 if a system of equations has a unique solution?

Back

If the lines intersect at exactly one point, the system has a unique solution.

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What is the first step in 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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If you substitute a value into an equation and get a true statement, what does that indicate?

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It indicates that the substituted value is a solution to the equation.

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What is the graphical representation of a system of equations?

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The graphical representation consists of lines or curves that may intersect at points.

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What is the significance of the point of intersection in a system of equations?

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It represents the solution to the system, where all equations are satisfied.