Writing System of Linear Equations

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables. The solution to the system is the point(s) where the equations intersect on a graph.

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How do you represent a word problem as a system of equations?

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To represent a word problem as a system of equations, identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the total quantities and values described in the problem.

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What does the slope of a line represent in a linear equation?

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The slope of a line in a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how much y changes for a unit change in x.

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What is the y-intercept in a linear equation?

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The y-intercept is the point where the line crosses the y-axis. In the equation y = mx + b, 'b' represents the y-intercept.

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How can you determine if a system of equations has one solution, no solution, or infinitely many solutions?

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A system has one solution if the lines intersect at a single point, no solution if the lines are parallel (same slope, different y-intercepts), and infinitely many solutions if the lines are the same (coincident lines).

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What is the substitution method for 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 both variables.

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What is the elimination method for 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 do you convert a word problem into a linear equation?

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To convert a word problem into a linear equation, identify the quantities involved, assign variables, and translate the relationships and operations described in the problem into mathematical expressions.

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What is the significance of the coefficients in a linear equation?

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The coefficients in a linear equation represent the rate of change of the dependent variable with respect to the independent variable. They indicate how much the dependent variable changes when the independent variable increases by one unit.

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What is a linear equation in two variables?

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A linear equation in two variables is an equation that can be written in the form Ax + By = C, where A, B, and C are constants, and x and y are the variables.