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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To solve a system of linear 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 linear equations?

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The graphical representation of a system of linear equations consists of the lines corresponding to each equation. The point(s) where the lines intersect represent the solution(s) of the system.

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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 a dependent system of equations?

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A dependent system of equations has infinitely many solutions, as the equations represent the same line.

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What is an independent system of equations?

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An independent system of equations has exactly one solution, as the lines intersect at a single point.

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What is an inconsistent system of equations?

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An inconsistent system of equations has no solution, as the lines are parallel and never intersect.

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How do you write a linear equation from a word problem?

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To write a linear equation from a word problem, identify the variables, translate the relationships and conditions into mathematical expressions, and form an equation.

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What is the slope-intercept form of a linear equation?

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The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.