6.5 - Applying 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.

Front

What is the substitution method in solving linear equations?

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A method where one equation is solved for one variable, and that expression is substituted into the other equation.

Front

What is the elimination method in solving linear equations?

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A method that involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

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What is the graphical method for solving linear equations?

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

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

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The system has no solution because the lines never intersect.

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

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The system has infinitely many solutions because the lines are the same.

Front

What is the first step in using the elimination method?

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

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How do you determine the best method to solve a system of linear equations?

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Consider the complexity of the equations and the number of variables; choose substitution for simpler equations and elimination for more complex ones.

Front

What is the solution to the system: 2x + 3y = 6 and x - y = 1?

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x = 3, y = 0.