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Published byShanon Hicks Modified over 6 years ago

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Solving Linear Systems of Equations - Concept Consider the following set of equations: Such a set is called a Linear System of Equations in two variables. Note that both variables in both equations are degree one (exponent of 1), thus the name linear.

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Take just the first equation by itself. Find some ordered pairs that satisfy the equation. (-1, -1) ( 0, 1/2) ( 1, 2) (2, 7/2) Each ordered pair that satisfies the equation is called a solution of the equation.

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Solutions to the second equation could be found in the same way. Now consider again the system of equations. The solution to the system of equations is any ordered pair ( a, b) that satisfies both equations.

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x = 1 ( 1, 2) ( 1, 2) x-value of point First Equation Second Equation x = - 1 (-1, -1) (-1, 6) x = 0 ( 0, 1/2) ( 0, 4) x = 2 ( 2, 7/2) ( 2, 0) Notice that ( 1, 2) is the only ordered pair that is a solution for both equations. Thus, ( 1, 2) is a solution to the system of equations.

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