Systems of Equations

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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 is the graphical representation of a system of equations?

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The graphical representation is the intersection point(s) of the lines or curves represented by the equations.

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What is the substitution method in solving systems of equations?

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

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What is the elimination method in solving systems of equations?

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

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A system has no solution if the equations represent parallel lines that never intersect.

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

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

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What is the point of intersection in a system of equations?

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The point of intersection is the solution to the system, representing the values of the variables that satisfy all equations.

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The solution is (3, 0).

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The first step is to isolate the variable p by moving all terms involving p to one side.