Systems of Linear Equations

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What is a system of linear equations?

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A set of two or more linear equations with the same variables.

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What does it mean to solve a system of linear equations?

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Finding the values of the variables that satisfy all equations in the system.

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

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Plotting the equations on a graph and identifying the point(s) where they intersect.

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What is the elimination method in solving systems of linear equations?

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A method that involves adding or subtracting equations to eliminate one variable.

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What is the substitution method in solving systems of linear equations?

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A method where one equation is solved for one variable, which is then substituted into the other equation.

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What does it mean if a system of linear equations has no solution?

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The lines representing the equations are parallel and never intersect.

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What does it mean if a system of linear equations has infinitely many solutions?

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The equations represent the same line, meaning every point on the line is a solution.

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How do you determine the solution of a system of equations graphically?

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The solution is the point where the graphs of the equations intersect.

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What is the first step in solving a system of equations by elimination?

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Align the equations so that corresponding variables and constants are in the same columns.

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What is the purpose of rearranging equations in the substitution method?

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To express one variable in terms of the other, making substitution easier.