Solving 3 Variable Systems of Equations using Substitution

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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 set of values that satisfy all equations simultaneously.

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What does substitution mean in the context of solving equations?

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Substitution is a method where one variable is expressed in terms of another variable, allowing for the replacement of that variable in other equations.

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How do you isolate a variable in an equation?

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To isolate a variable, you manipulate the equation using algebraic operations (addition, subtraction, multiplication, division) to get the variable on one side of the equation by itself.

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

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The first step is to solve one of the equations for one variable in terms of the others.

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z = -5.

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The solution is (5, 7, 2).

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How do you check if a solution is correct for a system of equations?

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To check if a solution is correct, substitute the values of the variables back into the original equations. If all equations are satisfied, the solution is correct.

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What does it mean if a system of equations has no solution?

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A system of equations has no solution if the equations represent parallel lines (in two dimensions) or planes (in three dimensions) that never intersect.

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What does it mean if a system of equations has infinitely many solutions?

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A system of equations has infinitely many solutions if the equations represent the same line or plane, meaning they overlap completely.