Solving Systems by Substitution

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

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

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

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

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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.

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How do you determine the number of solutions in a system of equations?

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By analyzing the graphs of the equations: intersecting lines (one solution), parallel lines (no solution), or the same line (infinite solutions).

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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 in terms of the other.