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 for a system of equations to have a solution?

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It means there is at least one set of values for the variables that satisfies all equations in the system.

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What does it mean if two lines intersect on a graph?

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The system of equations has one unique solution, which is the point of intersection.

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What does it mean if two lines are parallel on a graph?

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The system of equations has no solution because the lines never intersect.

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What does it mean if two lines coincide on a graph?

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The system of equations has infinitely many solutions because the lines are the same.

Front

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

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By finding the point where the lines representing the equations 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.

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What is the elimination method 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 is the graphical method of solving systems of equations?

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

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What is a unique solution in the context of systems of equations?

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A unique solution occurs when the lines intersect at exactly one point.