Summary of Simultaneous Equations


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  • Finding the solution by the method of substitution.
  • Finding the solution by the method of substitution.

(i) Coefficients of one of the variables (say x) in the two equations are made equal, by multiplying them with suitable factors.

(ii) By addition or subtraction, this variable (x) is eliminated.

(iii) The value of the other variable (y) is obtained and by substitution we obtain x.

  • Method of substitution

We get x in terms of y (or y in terms of x) from one of the equations and substitute in the other equation. Thus one of the variables is eliminated and we proceed as in the previous case.

  • In problems involving two unknowns, we replace them by x and y. We express the given conditions algebraically in the form of two linear equations and solve for x and y.


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