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 that are solved together.

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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 graphical representation of a system of equations?

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

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What is the substitution method?

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A method of solving a system of equations by solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method?

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A method of solving a system of equations by adding or subtracting the equations to eliminate one variable.

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What is an independent system of equations?

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A system that has exactly one solution, where the lines intersect at a single point.

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What is a dependent system of equations?

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A system that has infinitely many solutions, where the equations represent the same line.

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What is an inconsistent system of equations?

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A system that has no solution, where the equations represent parallel lines.

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

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By plotting the equations on a graph and identifying the intersection point.

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What is the first step in solving a system of equations by substitution?

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Isolate one variable in one of the equations.