Algebraic Methods Of Solving Simultaneous Equations

As indicate earlier there can be both graphics as well as algebraic methods of solving simultaneous equations and therefore, employed quite often in linear and non-linear programming. The graphics method is also employed in case of inequalities. We illustrate below its use when the simultaneous equations consist of both linear and non-linear equations.


The point of intersection gives a common solution to the two equations, one of which is linear (y=3x+3) and other one cubic (y=x cube). The value of x=2.1 gives an approximate solution which is good enough for business decision making.

We now discus the algebraic method of solving such equation. The use of metrics for the same shall be dealt in relevant chapter. Various method are indicated depending on the combination of linear with linear or non linear equations.

There are three methods of Simultaneous Equation

(A) When Both Equations are Linear

• Method of substitution
• Method of Elimination
• Method of Cross Multiplication

(B) When one equation is linear and the other one is quadratic

(C) When both equations are quadratic


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