8.9A Simultaneous Linear Equations

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What are simultaneous linear equations?

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Simultaneous linear equations are a set of equations with multiple variables that are solved together, where the solution satisfies all equations in the set.

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What does the solution of a system of equations represent?

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The solution of a system of equations represents the point(s) at which the graphs of the equations intersect, indicating the values of the variables that satisfy all equations.

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How can you represent the solution of simultaneous equations?

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The solution can be represented as an ordered pair (x, y), where x and y are the values of the variables that satisfy the equations.

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What is the graphical representation of simultaneous linear equations?

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The graphical representation consists of lines on a coordinate plane, where the intersection point(s) of the lines represent the solution(s) of the equations.

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What methods can be used to solve simultaneous linear equations?

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Common methods include substitution, elimination, and graphing.

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What is the substitution method in solving simultaneous equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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What is the elimination method in solving simultaneous 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 simultaneous equations?

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If two lines are parallel, it means there is no solution to the system of equations, as the lines never intersect.

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What does it mean if two lines coincide in the context of simultaneous equations?

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If two lines coincide, it means there are infinitely many solutions, as every point on the line is a solution to the system.

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How do you check if your solution to simultaneous equations is correct?

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