Systems of Equations And Inequalities

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What is a system of equations?

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A system of equations is 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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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What are the three methods to solve a system of equations?

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1. Graphing 2. Substitution 3. Elimination

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What is the substitution method?

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The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

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What is the elimination method?

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

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What is an inconsistent system of equations?

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An inconsistent system of equations is one that has no solution, meaning the lines represented by the equations are parallel.

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What is a consistent system of equations?

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A consistent system of equations has at least one solution, which can be either one unique solution or infinitely many solutions.

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What is a dependent system of equations?

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A dependent system of equations has infinitely many solutions, meaning the equations represent the same line.

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How do you graph a system of equations?

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To graph a system of equations, plot each equation on the same coordinate plane and identify the point(s) where they intersect.

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

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The solution to a system of equations is represented by the point(s) where the graphs of the equations intersect.