Writing Systems of Linear Equations

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What is a linear equation?

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A linear equation is an equation that represents a straight line when graphed. It can be written in the form ax + by = c, where a, b, and c are constants.

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What does it mean to solve a system of linear equations?

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Solving a system of linear equations means finding the values of the variables that satisfy all equations in the system simultaneously.

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What is the substitution method in solving linear 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 linear 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 the meaning of 'c' and 'a' in the context of ticket sales?

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In the context of ticket sales, 'c' typically represents the number of children tickets sold, while 'a' represents the number of adult tickets sold.

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How do you write a system of equations from a word problem?

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To write a system of equations from a word problem, identify the variables, translate the relationships and conditions into equations, and ensure the equations represent the same scenario.

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What is the significance of coefficients in a linear equation?

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Coefficients in a linear equation represent the rate of change or the weight of each variable in the equation.

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What does it mean if two lines are parallel in a system of equations?

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If two lines are parallel, it means that the system of equations has no solution, as the lines never intersect.

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What does it mean if two lines intersect at a point in a system of equations?

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If two lines intersect at a point, it means that the system of equations has a unique solution, which is the coordinates of the intersection point.

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What is a consistent system of equations?

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