Systems of Linear Equations (Two Variables)

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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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How can you represent a solution to a system of linear equations?

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A solution to a system of linear equations with two variables is represented as an ordered pair (x, y).

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What does it mean for a solution to satisfy a system of equations?

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A solution satisfies a system of equations if it makes all equations in the system true when the values of x and y are substituted.

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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).

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What is the substitution method for solving systems of 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 for solving systems of 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 other variable.

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What does it mean if two lines are parallel in the context of a system of linear 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 coincide in the context of a system of linear equations?

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If two lines coincide, it means that the system of equations has infinitely many solutions, as every point on the line is a solution.

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What is the importance of checking solutions in a system of linear equations?

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Checking solutions ensures that the values satisfy all equations in the system, confirming that the solution is correct.

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How do you determine if a system of equations is consistent or inconsistent?

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A system is consistent if it has at least one solution; it is inconsistent if it has no solutions.