Methods to Solve Simultaneous Equations


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Consider a linear equations in two variables, say, 3x - 2y = 5. It has an infinite number of solutions, some of these are x = 0, Consider a linear equations in two variables, say, 3x - 2y = 5. It has an infinite number of solutions, some of these are x = 0,

y = 0. Similarly, if we take another equation 2x - y = 3, it also has an infinite number of solutions. Solving two equations simultaneously means to find the common solution of both the equations, i.e., a solution which satisfies both the equations. (Such a common solution, if it exists, can be shown to be unique.)

For the above two equations, x = 1 and y = -1 is the only common solution.

The following two methods are used to find a solution:

(a) Method of elimination

(b) Method of substitution.



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