# Solution of the linear system of two equations in two unknowns by the Elimination method

Apr 15th, 2015
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Solution of the linear system of two equations in two unknowns by the EliminationmethodThis lesson describes the Elimination method for solving the linear system of two equations in twounknowns.The method is to multiply both sides of the first equation to some number, to multiply both sides ofthe second equation to another number and then to add both these equations (or to subtract one equationfrom another). The multipliers are selected to cancel co-named variable terms in the final equation forsome variable.When this is done, you can easily solve the obtained equation for the remaining variable, backsubstitute the found value to either of the original equations and to find the value of the variable that waseliminated at the first step.Examples below show how this method works.Example 1Solve the system of equationsMultiply the first equation by 2 (which means "Multiply both sides of the first equation by 2"). Leave thesecond equation as is. You will get:.Add the first and the second equations (which means "Add left sides and add right sides of the first and thesecond equations"). You will get:.The solution of this equation isBack-substitute this value of,.to the first (original) equation. You will get:and then.The solution of this equation is.Now, check the calculated solution. Simply substitute the found values oforiginal equations. You will getandto thefor the left side of the first equation, and this is identical to its right sid

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