Applications & 3 Variable Systems

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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 to the system is the set of values that satisfy all equations simultaneously.

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What does it mean for a system of equations to have one solution?

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A system of equations has one solution when the graphs of the equations intersect at exactly one point, indicating a unique solution for the variables.

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How do you determine 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, which means they never intersect.

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What is the graphical representation of a system of equations with infinitely many solutions?

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The graphical representation of a system with infinitely many solutions is when the equations represent the same line, meaning every point on the line is a solution.

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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 then substituting that expression into the other equation to find the values of the variables.

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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 remaining variable.

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How can you check if your solution to a system of equations is correct?

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You can check your solution by substituting the values back into the original equations to see if they satisfy all equations.

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What is the significance of coefficients in a system of equations?

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Coefficients represent the numerical factors of the variables in the equations and determine the slope and position of the lines when graphed.

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What is a linear equation?

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A linear equation is an equation that forms a straight line when graphed, typically in the form of y = mx + b, where m is the slope and b is the y-intercept.

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What is the cost equation for ticket sales based on the given problem?

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The cost equation can be represented as 4a + 7s = total revenue, where 'a' is the number of adult tickets and 's' is the number of student tickets.