5.3 PRACTICE - 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 y = mx + b, where m is the slope and b is the y-intercept.

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

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Identify the variables, translate the relationships and conditions into equations, and ensure the equations reflect the problem's constraints.

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

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Coefficients represent the rate of change of the dependent variable with respect to the independent variable in a linear 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 they have the same slope but different y-intercepts, indicating that there is no solution to the system.

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

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If two lines intersect, it means there is exactly one solution to the system, which is the point of intersection.

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What is the graphical method of solving a system of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) where the lines intersect.

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How can you check the solution of a system of equations?

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You can check the solution by substituting the values back into the original equations to see if they hold true.

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