Solving Systems of Equations

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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 solution of a system of equations?

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The point(s) where the graphs of the equations intersect.

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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, so every point on the line is a solution.

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How can you graphically represent a system of equations?

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By plotting the equations on the same coordinate plane and observing their intersections.

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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 both equations on a graph and identifying the point of intersection.