Writing 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 set of values that satisfy all equations in the system.

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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 make all equations true simultaneously.

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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.

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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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What is a linear equation?

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A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is the meaning of 'c' and 's' in the context of a restaurant bill problem?

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In the restaurant bill problem, 'c' represents the number of chicken orders and 's' represents the number of steak orders.

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How do you represent a total number of items in a system of equations?

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You can represent a total number of items by creating an equation that sums the quantities of each item, such as c + s = total.

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What does it mean if two equations in a system are dependent?

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If two equations are dependent, they represent the same line and have infinitely many solutions.

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What does it mean if two equations in a system are independent?

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If two equations are independent, they represent different lines and typically have one unique solution.

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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, meaning the lines intersect at one or more points.