Solution of the linear system of two equations in two unknowns by the Substitution method

Apr 15th, 2015
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Solution of the linear system of two equations in two unknowns by the Substitution method

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Solution of the linear system of two equations in two unknownsby the Substitution methodThis lesson describes the Substitution method for solving the linear system of twoequations with two unknowns.The method is to express one variable via another using one equation and then tosubstitute this expression into another equation. In this way you reduce the originalsystem of two equations with two unknowns to the single equation with one unknown.When this reduction is done, simplify the obtained equation and solve it.After completing this, back-substitute the found value to either of the original equationsand find the value of the remaining variable.Examples below show how this method works.Example 1Solve the system of equationsExpressfrom the first equation:.Substitute this to the second equation:.Simplify the last equation by collecting common terms and solve it for,,,,.Back-substitute this value of.to the first original equation::Simplify and solve this equation for.:Thus, the solution of the original system of equations is,.Now, check the calculated solution. Simply substitute the found values ofinto the original equations. You will getandfor the left side of the first equation, and this is identical to itsright side;for the left side of the second equation, and this is identical toits right side.The check shows that the solution is correct.Example 2Solve the system of equationsExpressfrom the second equation:.

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