Solving Systems 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 is the point(s) where the equations intersect.

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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 linear equation in slope-intercept form?

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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 lines on a coordinate plane, where the intersection point(s) represent the solution(s) of the system.

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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 the system has no solution.

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

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system.

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

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To check the solution, substitute the values of the variables back into the original equations to see if they hold true.

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What is the first step in using the substitution method?

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The first step in using the substitution method is to solve one of the equations for one variable in terms of the other variable.