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 substitution 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.

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What is elimination in solving systems of equations?

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A method where equations are added or subtracted 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 one solution?

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The lines representing the equations intersect at exactly one point.

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

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The lines representing the equations are the same line, meaning they overlap completely.

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

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By analyzing the slopes and y-intercepts of the lines represented by the equations.

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What is the graphical representation of a system of equations?

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The intersection points of the lines representing the equations on a coordinate plane.

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What is the first step in solving a system of equations by substitution?

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Isolate one variable in one of the equations.