Solving Systems of Linear Equations

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What is a system of linear equations?

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A set of two or more linear 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 make all equations true simultaneously.

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What is the graphical representation of a system of linear equations?

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The intersection point(s) of the lines representing the equations.

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What are the possible outcomes when solving a system of linear equations?

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1. One solution (intersecting lines) 2. No solution (parallel lines) 3. Infinite solutions (same line)

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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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How do you determine if a system of equations has no solution?

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If the equations represent parallel lines, they will never intersect.

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How do you determine if a system of equations has infinite solutions?

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If the equations represent the same line, every point on the line is a solution.

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What is an ordered pair in the context of systems of equations?

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A pair of numbers (x, y) that represents a point on the coordinate plane.

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What does it mean for an ordered pair to be a solution to a system of equations?

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It means that substituting the values of the ordered pair into both equations makes them true.