M2T3 Flashcard: 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. The solution is the point(s) where the equations intersect.

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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 simultaneously.

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What is the elimination method in solving systems of equations?

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A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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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 an ordered pair?

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A pair of numbers (x, y) that represent a point in a two-dimensional space.

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How do you graph a system of equations?

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By plotting each equation on the same coordinate plane and identifying the point(s) where they intersect.

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What does it mean if two lines are parallel in a system of equations?

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The system has no solution because the lines never intersect.

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What does it mean if two lines coincide in a system of equations?

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

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What is the graphical representation of the solution to a system of equations?

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

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What is an inequality?

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A mathematical statement that compares two expressions, indicating that one is greater than, less than, or not equal to the other.