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. 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 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 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 infinitely many solutions?

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

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How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

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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 graphs of the equations plotted on a coordinate plane, showing their intersection points.

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The best method is elimination.