SIMULTANEOUS EQUATIONS Algebra3x4y7(x5y12)4x9y19Adding the second equation to the first corresponds to adding the same quantity to both sides ofthe first equation. Thus, the resulting equation is still true. Similarly, two equations can besubtracted.4x3y8(2x5y11)2x8y3Subtracting the second equation from the first corresponds to subtracting the same quantity fromboth sides of the first equation. Thus, the resulting equation is still true.The basic approach used to solve a system of equations is to reduce the system by eliminatingthe unknowns one at a time until one equation with one unknown results. This equation is solvedand its value used to determine the values of the other unknowns, again one at a time. There arethree different techniques used to eliminate unknowns in systems of equations: addition orsubtraction, substitution, and comparison.SolvingSimultaneousEquationsThe simplest system of equations is one involving two linear equations with two unknowns.5x + 6y = 123x + 5y = 3The approach used to solve systems of two linear equations involving two unknowns is tocombine the two equations in such a way that one of the unknowns is eliminated. The resultingequation can be solved for one unknown, and either of the original equations can then be usedto solve for the other unknown.Systems of two equations involving two unknowns can be solved by addition or subtraction usingfive steps.Step 1. Multiply or divide one or both equations by some factor or factors thatwill make the coefficients of one unknown numerically equal in bothequations.Step 2. Eliminate the unknown having equal coefficients by addition orsubtraction.Step 3. Solve the resulting equation for the value of the one remaining unknown.MA-02 Page 32 Rev. 0
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